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Advances in Geographical and Environmental Sciences
Swapan Kumar Maity
Essential 
Graphical 
Techniques in 
Geography
Advances in Geographical and Environmental
Sciences
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R. B. Singh, University of Delhi, Delhi, India
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Swapan Kumar Maity
Essential Graphical
Techniques in Geography
Swapan Kumar Maity
Department of Geography
Nayagram P.R.M. Government College
Jhargram, West Bengal, India
ISSN 2198-3542 ISSN 2198-3550 (electronic)
Advances in Geographical and Environmental Sciences
ISBN 978-981-16-6584-4 ISBN 978-981-16-6585-1 (eBook)
https://doi.org/10.1007/978-981-16-6585-1
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Dedicated to my Parents
Preface
Geography is a scientific discipline that emphasizes how and why different
geographic features vary from one place to another and how spatial patterns of
these features change with time. Geographers always concentrate on the explanation
of how physical and cultural features are distributed on the earth surface and what
kinds of factors and processes are responsible for their spatial and temporal varia-
tions. Geographical data need appropriate, systematic and logical presentation for
a better understanding of their cartographic characteristics. Suitable, accurate and
lucid demonstration and visualization of geographical data become helpful for their
correct analysis, explanation and realization. Therefore, various types of primary and
secondary data are used voluminously to explain and analyze the spatial distributions
and variations of different geographical events and phenomena.
Graphs, diagrams and maps are three unique and distinctive techniques of visu-
alization of geographical data. In narrow sense, graphical representation means the
depiction of data using various types of graphs but in a wider sense, all types of
graphs, diagrams and mapping techniques are included in graphical methods of
portraying the data. Graphical representation of various kinds of geographical data
is very simple, attractive and easily understandable not only to the geographers or
efficient academicians but also to the common literate people. It is the key for geog-
raphers and researchers to recognize the nature of data, the pattern of spatial and
temporal variations and their relationships and the formulation of principles to accu-
rately understand and analyze features on or near the earth’s surface. These modes of
representation also enable the development of spatial understanding and the capacity
for technical and logical decision making.
In this book, attempts have been made to analyze and explain different kinds of
graphs, diagrams and mapping techniques, which are extensively used for the visual
representation of various types of geographical data. The book has broadly been
divided into four main chapters. Chapter 1 emphasizes the discussion of the concept
and types of geographical data, major differences between them, sources of each type
of data, methods of their collection, classification and processing of the collected data
with special emphasis on frequency distribution table, methods and appropriateness
of representation of data and advantages and disadvantages of using these methods.
vii
viii Preface
It includes the discussion of the concept of attribute and variable, types of variables
and differences between them. It also explains different types of measurement scales
used in geographical analysis.
Chapter 2 includes the detailed classification of all types of graphs and types of
co-ordinate systems with illustrations as an essential basis of construction of graphs.
Different types of Bi-axial (Arithmetic andLogarithmic graph, Climograph etc.), Tri-
axial (Ternary graph), Multi-axial (Spider graph, Polar graph etc.) and specialgraphs
(Water budget graph, Hydrograph, Rating curve, Lorenz curve, Rank-size graph,
Hypsometric curve etc.) have been discussed with suitable examples in terms of their
appropriate data structure, necessary numerical calculations, methods of construc-
tion, proper illustrations and advantages and disadvantages of their use. Concept of
arithmetic and logarithmic graphs has been explained precisely with pertinent exam-
ples and illustrations. Different types of frequency distribution graphs have been
explained with suitable data, necessary mathematical and statistical computations
and proper illustrations.
Chapter 3 focuses on the detailed discussion of various types of diagrams clas-
sified on a different basis. All types of one-dimensional (Bar, Pyramid etc.), two-
dimensional (Triangular, Square, Circular etc.), three-dimensional (Cube, Sphere
etc.) and other diagrams (Pictograms and Kite diagram) have been discussed with
suitable examples in terms of their appropriate data structure, necessary numerical
(geometrical) calculations, methods of construction, appropriate illustrations and
advantages and disadvantages of their use.
Chapter 4 explains the basic Cartographic terminologies like Geodesy, Geoid,
Spheroid, Datum, Geographic co-ordinate system, Surveying and levelling,
Traversing, Bearing, Magnetic declination and inclination etc in a lucid manner
with suitable illustrations. It includes the detailed classification and discussion of
all types of maps based on their scale and purposes (contents) of preparing the map
with special emphasis on Indian Topographical Sheets. All pictorial and mathemat-
ical methods of representation of relief have been explained in detail with suitable
examples and illustrations. Various types of distributional thematic maps have been
analyzed with suitable examples emphasizing their suitable data structure, neces-
sary numerical calculations, methods and principles of their construction, proper
illustrations and advantages and disadvantages of their use. It also explains different
techniques of measurement of direction, distance and area on maps.
The methods of construction of all types of graphs, diagrams and maps are
explained step-by-step in a systematic way for easy and quick understanding of the
readers. The book is unique of its kind as it reflects an accurate co-relation between
the theoretical knowledge of various geographical events and phenomena and their
realistic implications with suitable examples using proper graphical techniques. The
book will be helpful for the students, researchers, cartographers and decision-makers
in representing and analyzing various geographical data for a better, systematic and
scientific understanding of the real world.
Midnapore, West Bengal, India Swapan Kumar Maity
Acknowledgements
It gives me immense pleasure to express my deep gratitude to all those who
contributed in their own ways for the successful completion of this book. I am
heartily thankful to each soul that has come across all through the journey.
I owe my thankfulness to my students Rajesh Bag, Gopal Shee, Baneswar
Adak, Suvajit Barman (SACT, K. D. College of Commerce and General Studies),
Krishnapriyo Das and Arpita Routh for their help and support in preparing this book.
I would like to express my gratitude to Dr. Samit Maiti, Assistant Professor
of English, Seva Bharati Mahavidyalaya and Dr. Soumitra Chakraborty, Assis-
tant Professor of English, Mallabhum Institute of Technology for their academic
support and advice. I am really thankful to Mr. Titas Aikat, GIS Manager, Horizen,
Naihati and Mrs. Somrita Sinha, SACT, Department of Geography, Raja N. L.
Khan Women’s College for their technical and academic support for preparing this
book. I am also thankful to Dr. Netai Chandra Das, Officer-in-Charge and Assistant
Professor of Philosophy, Nayagram P. R. M. Government College for his continuous
encouragement and valuable suggestions.
I would like to express my heartfelt gratitude to Dr. Ramkrishna Maiti, Professor,
Department of Geography and Environment Management, Vidyasagar University
for his encouragement, support and advice. His valuable suggestions at the time of
preparing this book helped me in bringing it to the final shape.
I convey a lot of thanks to all my family members, especially to my wife Sonali
for her encouragement, co-operation and continuous moral and emotional supports.
I am very much thankful to my little son Souparno for his co-operation, which has
given me sufficient time for the completion of this book.
Midnapore, West Bengal, India Swapan Kumar Maity
ix
About This Book
Representation of geographical data using graphs, diagrams andmapping techniques
is a key for geographers and for researchers in other disciplines to explore the nature
of data, the pattern of spatial and temporal variations and their relationships and
formulation of principles to accurately understand and analyze features on or near
the earth’s surface. These modes of representation also enable the development of
spatial understanding and the capacity for technical and logical decision-making.
The book depicts all types of graphs, diagrams and maps, explained in detail with
numerous examples. The emphasis is on their appropriate data structure, the rele-
vance of selecting the correct technique, methods of their construction, advantages
and disadvantages of their use and applications of these techniques in analyzing
and realizing the spatial pattern of various geographical features and phenomena.
This book is unique in that it reflects an accurate correlation between theoretical
knowledge of geographical events and phenomena and their realistic implications,
with relevant examples using appropriate graphical methods. The book serves as
a valuable resource for students, researchers, cartographers and decision-makers to
analyze and represent various geographical data for a better, systematic and scientific
understanding of the real world.
xi
Contents
1 Concept, Types, Collection, Classification and Representation
of Geographical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Concept of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Concept of Geographical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Types of Data (Geographical Data) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Qualitative Data (Attribute) . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.2 Quantitative Data (Variable) . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4.3 Uni-Variate Data and Bi-Variate Data . . . . . . . . . . . . . . . . . 5
1.4.4 Difference Between Uni-Variate Data
and Bi-Variate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.5 Independent Variable and Dependent Variable . . . . . . . . . . 7
1.4.6 Difference Between Qualitative Data (Attribute)
and Quantitative Data (Variable) . . . . . . . . . . . . . . . . . . . . . 7
1.4.7 Primary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.8 Secondary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.9 Advantages of Use of Primary Data Over
the Secondary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.10 Difference Between Primary and Secondary Data . . . . . . . 9
1.5 Methods of Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Methods of Primary Data Collection . . . . . . . . . . . . . . . . . . 10
1.5.2 Methods of Secondary Data Collection . . . . . . . . . . . . . . . . 17
1.6 Measurement Scales in Geographical System . . . . . . . . . . . . . . . . . . 19
1.6.1 Nominal Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6.2 Ordinal Scale . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6.3 Interval Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6.4 Ratio Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.7 Processing of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.7.1 Classification of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7.2 Tabulation of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.7.3 Frequency Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
xiii
xiv Contents
1.8 Methods of Presentation of Geographical Data . . . . . . . . . . . . . . . . . 42
1.8.1 Textual Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.8.2 Tabular Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.8.3 Semi-Tabular Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.8.4 Graphical Form (Graphs, Diagrams and Maps) . . . . . . . . . 45
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2 Representation of Geographical Data Using Graphs . . . . . . . . . . . . . . . 47
2.1 Concept of Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 Types of Co-ordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.1 Cartesian or Rectangular Co-ordinate System . . . . . . . . . . 48
2.2.2 Polar Co-ordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.3 Cylindrical Co-ordinate System . . . . . . . . . . . . . . . . . . . . . . 52
2.2.4 Spherical Co-ordinate System . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 Selection of Scale in Constructing a Graph . . . . . . . . . . . . . . . . . . . . 55
2.4 Advantages and Disadvantages of the Use of Graphs . . . . . . . . . . . 55
2.5 Types of Graphical Representation of Data . . . . . . . . . . . . . . . . . . . . 56
2.5.1 Bi-axial Graphs or Line Graphs or Historigram . . . . . . . . . 56
2.5.2 Tri-axial Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.5.3 Multi-axial Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.5.4 Special Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.5.5 Frequency Distribution Graphs . . . . . . . . . . . . . . . . . . . . . . . 132
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
3 Diagrammatic Representation of Geographical Data . . . . . . . . . . . . . . 153
3.1 Concept of Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
3.2 Advantages and Disadvantages of Data Representation
in Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
3.3 Difference Between Graph and Diagram . . . . . . . . . . . . . . . . . . . . . . 154
3.4 Types of Diagrams in Data Representation . . . . . . . . . . . . . . . . . . . . 155
3.4.1 One-Dimensional Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.4.2 Two-Dimensional Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 168
3.4.3 Three-Dimensional Diagrams . . . . . . . . . . . . . . . . . . . . . . . . 182
3.4.4 Other Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
4 Mapping Techniques of Geographical Data . . . . . . . . . . . . . . . . . . . . . . . 193
4.1 Concept and Definition of Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.2 Concept of Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
4.3 Difference Between Plan and Map . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
4.4 Elements of a Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
4.5 History of Map-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
4.5.1 Ancient Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.5.2 Mediaeval Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.5.3 Modern Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
4.5.4 Contributions of Indian Scholars . . . . . . . . . . . . . . . . . . . . . 200
Contents xv
4.6 Methods of Mapping the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
4.7 Cartography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
4.8 Key Concepts of Cartography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
4.8.1 Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
4.8.2 Geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
4.8.3 Ellipsoid or Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
4.8.4 Surveying and Levelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.8.5 Geodetic Surveying and Plane Surveying . . . . . . . . . . . . . . 209
4.8.6 Datum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
4.8.7 Reduced Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
4.8.8 Geographic Co-ordinate System . . . . . . . . . . . . . . . . . . . . . 212
4.8.9 Cardinal Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
4.8.10 Map Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.8.11 Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.8.12 Magnetic Declination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
4.8.13 Magnetic Inclination or Magnetic Dip . . . . . . . . . . . . . . . . 223
4.8.14 Traversing or Traverse Survey . . . . . . . . . . . . . . . . . . . . . . . 224
4.8.15 Triangulation Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
4.8.16 Trilateration Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
4.8.17 Difference Between Triangulation and Trilateration
Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
4.9 Types of Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
4.9.1 General Reference Maps (General Purpose Maps) . . . . . . 229
4.9.2 Thematic Maps (Special Purpose Maps) . . . . . . . . . . . . . . . 230
4.9.3 Types of Thematic Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
4.10 Types of Maps Based on Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
4.10.1 Large-Scale Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
4.10.2 Small-Scale Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
4.10.3 Medium-Scale Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
4.11 Based on the Purpose or Content or Function of the Map . . . . . . . . 238
4.11.1 Physical or Natural Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
4.11.2 Cultural Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
4.12 Techniques for the Study of Spatial Patterns of Distribution
of Elements (Distribution Map) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
4.12.1 Chorochromatic Map (Colour or Tint Method) . . . . . . . . . 252
4.12.2 Choroschematic or Symbol Map . . . . . . . . . . . . . . . . . . . . . 255
4.12.3 Choropleth Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 258
4.12.4 Dasymetric Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
4.12.5 Isarithmic Map (Isometric Map and Isopleth Map) . . . . . . 266
4.12.6 Dot Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
4.12.7 Flow Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
4.12.8 Diagrammatic Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
4.13 Importance and Uses of Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
4.13.1 Measurement of Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
4.13.2 Measurement of Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
xvi Contents
4.13.3 Measurement of Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
About the Author
Dr. Swapan KumarMaity is an assistant professor of geography at Nayagram P. R.
M. Government College, Jhargram, West Bengal, India. He completed his doctoral
degree at Vidyasagar University with his dissertation titled Mechanisms of sedimen-
tation in the lower reach of the Rupnarayan River. Dr. Maity has 7 years of teaching
experience at the undergraduate level in geography and 2 years at the postgraduate
level in geography and environmental management. His teaching interests include
geotectonic, geomorphology, climatology and practical geography, including remote
sensing and GIS. His main research areas include fluvial geomorphology, river sedi-
mentation and sediment mineralogy. He has published several research articles in
renowned journals and two books from Springer in the field of the mechanism and
environment of river sedimentation. Dr. Maity is a life member of the Indian Institute
of Geomorphologists.
xvii
Abbreviations
ADCP Acoustic Doppler Current Profiler
AE Actual evapotranspiration
BB Backward Bearing
CI Cropping Intensity
DMS Degrees, Minutes, and Seconds
DSMs Defence Series Maps
DST Department of Science and Technology
EGM 96 Earth Gravitational Model 1996
EI Erosional integral
FAO Food and Agricultural Organization
FB Forward Bearing
GCA Gross Cropped Area
GCS Geographic Co-ordinate System
GPS Global Positioning System
GRS-80 Geodetic Reference System 1980
GSI Geological Survey of India
GTS Great Trigonometrical Survey
HI Hypsometric integral
IMF International Monitory Fund
IQR Inter-quartile Range
ISI Indian Statistical Institute
MSL Mean Sea Level
NATMO National Atlas and Thematic Mapping Organization
NCA Net Cropped Area
NMP National Map Policy
NRSA National Remote Sensing Agency
OSMs Open Series Maps
PE Potential evapotranspiration
PWD Public Works Department
QB Quadrantal Bearing
RB Reduced Bearing
xix
xx Abbreviations
RL Reduced Level
SLR Satellite Laser Ranging
SOI Survey of India
UNO United Nations Organization
USDA United States Department of Agriculture
UTM Universal Transverse Mercator
VLBI Very Long Baseline Interferometry
WCB Whole Circle Bearing
WGS 84 World Geodetic System 1984
Symbols
fi Class frequency
xi Class mark
wi Class width
fdi Frequency density
R f i Relative frequency
N Total frequency
F Cumulative frequency
r Radial distance
θ Azimuthal angle
φ Polar angle or zenithal angle
δ Latitude
P Precipitation
T Temperature
R Soil moisture recharge
U Utilization of water
D Deficiency of water
S Surplus of water
Q Water discharge
G Gini co-efficient
Q1 Lower quartile
Q2 Middle quartile
Q3 Upper quartile
Pr Population of r ranking city
P1 Population of 1st ranking city
hi Mid-value of the contour height
H Maximum height of the basin
ai Area between successive contours
A Total basin area
Sk Skewness
β1 Skewness co-efficient
μ3 Third central moment
xxi
xxii Symbols
σ Population standard deviation
μ1 First moment
f (x) Probability density function
μ Population mean
β2 Kurtosis co-efficient
li Length of side of equilateral triangle or square or cube
ri Radius of the circle or sphere
f Flattening
e Eccentricity of the ellipse
H Topographic height or Orthometric height
h Spheroid or ellipsoid height
N Geoid height
I Magnetic inclination or magnetic dip
Z Vertical component
D Map distance
S Map scale
T Total number of full squares
List of Figures
Fig. 1.1 Qualitative classification of data (population) . . . . . . . . . . . . . . . . 27
Fig. 1.2 Different parts of an ideal table . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Fig. 2.1 Position of independent and dependent variables
in different quadrants (Cartesian co-ordinate system) . . . . . . . . . 49
Fig. 2.2 Determination of location of a point on Cartesian
co-ordinate system (3D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Fig. 2.3 Determination of location of a point on polar co-ordinate
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Fig. 2.4 Determination of location of a point on cylindrical
co-ordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Fig. 2.5 Determination of location of a point on spherical
co-ordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Fig. 2.6 Line graph (Historigram) showing the temporal changes
of total population in Kolkata Urban Agglomeration
(KUA) Source Census of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Fig. 2.7 Line graph or Historigram (Production of rice in India,
2000–2011) SourceDirectorate of Economics and Statistics
(Government of India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Fig. 2.8 a Arithmetic scale on both the axes, b Arithmetic scale
on the ‘X’-axis but the logarithmic scale on the ‘Y ’-axis, c
Arithmetic scale on the ‘Y ’-axis but the logarithmic scale
on the ‘X’-axis, and d Logarithmic scale on both the axes . . . . . 60
Fig. 2.9 Arithmetic graph (Number of male and female deaths
per year) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Fig. 2.10 Logarithmic graph (Number of male and female deaths
per year) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Fig. 2.11 Poly graph showing total, male and female literacy rates . . . . . . 66
Fig. 2.12 Band graph showing the production of various crops
in different years in India Source Directorate of Economics
and Statistics, Ministry of Agriculture and Farmers Welfare . . . . 68
Fig. 2.13 USDA type of climograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
xxiii
xxiv List of Figures
Fig. 2.14 The base frame of Foster’s climograph . . . . . . . . . . . . . . . . . . . . . 70
Fig. 2.15 Climograph showing the wet-bulb temperature and relative
humidity of Kolkata (after G. Taylor) . . . . . . . . . . . . . . . . . . . . . . 71
Fig. 2.16 Hythergraph showing the mean monthly temperature
and rainfall of Burdwan district . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Fig. 2.17 Identification of position of points in ternary graph . . . . . . . . . . . 74
Fig. 2.18 Identification of sediment type using ternary graph . . . . . . . . . . . 76
Fig. 2.19 Radar graph (Production of different crops) . . . . . . . . . . . . . . . . . 77
Fig. 2.20 Wind rose graph showing the percentage of days wind
blowing from different directions . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Fig. 2.21 Polar graph showing the number of corries facing
towards different directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Fig. 2.22 Scatter graph (Relation between the distance from CBD
and air temperature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Fig. 2.23 Positive, negative and no co-relation. . . . . . . . . . . . . . . . . . . . . . . 84
Fig. 2.24 Perfect positive and negative co-relation . . . . . . . . . . . . . . . . . . . . 85
Fig. 2.25 Linear and nonlinear co-relation . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Fig. 2.26 Ergograph showing the relation between seasons, climatic
elements and cropping patterns of Howrah, West Bengal . . . . . . 87
Fig. 2.27 Circular ergograph showing the rhythm of seasonal
activities (after A. Geddes and G.G. Ogilvie 1938) . . . . . . . . . . . 90
Fig. 2.28 Ombrothermic graph of Purulia district, West Bengal . . . . . . . . . 91
Fig. 2.29 Water balance curve of a sample study area . . . . . . . . . . . . . . . . . 96
Fig. 2.30 Elements of a hydrograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Fig. 2.31 Various components of run-off (after Singh 1994) . . . . . . . . . . . . 100
Fig. 2.32 Important components of streamflow hydrograph . . . . . . . . . . . . 101
Fig. 2.33 Rating curve (Relationship between stream stage
and discharge) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Fig. 2.34 Lorenz curve showing the inequality in the distribution
of number and area of land holdings . . . . . . . . . . . . . . . . . . . . . . . 109
Fig. 2.35 Lorenz curve showing the inequality in the distribution
of total and urban population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Fig. 2.36 Lorenz curve showing the inequality of income distribution
of people in Sweden, USA and India Sources Statistics
Sweden, online database (2014), U.S. Census Bureau,
Historical Income Tables (2016); Credit Suisse’s Global
Wealth Databook (2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Fig. 2.37 Rainfall dispersion graph of Bankura district (year 1976–
2015) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Fig. 2.38 Rank-size graph according to G.K. Zipf (arithmetic scale) . . . . . 118
Fig. 2.39 Rank-size graph according to Pareto (logarithmic scale) . . . . . . . 118
Fig. 2.40 Deviations in rank-size distribution . . . . . . . . . . . . . . . . . . . . . . . . 123
Fig. 2.41 Box-and-whisker graph without outliers . . . . . . . . . . . . . . . . . . . . 124
Fig. 2.42 Box-and-whisker graph with outliers . . . . . . . . . . . . . . . . . . . . . . . 124
Fig. 2.43 Hypsometric curve for the whole earth . . . . . . . . . . . . . . . . . . . . . 128
List of Figures xxv
Fig. 2.44 Sample drainage basin showing height and area . . . . . . . . . . . . . . 129
Fig. 2.45 Area–height relationship of the given drainage basin . . . . . . . . . . 129
Fig. 2.46 Hypsometric curve of the given drainage basin . . . . . . . . . . . . . . 130
Fig. 2.47 Understanding the stages of landform development using
hypsometric curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Fig. 2.48 Histogram (average concentration of SPM in the air) . . . . . . . . . 134
Fig. 2.49 Histogram (monthly income of families) . . . . . . . . . . . . . . . . . . . 135
Fig. 2.50 Frequency polygon showing the average concentration
of SPM in the air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Fig. 2.51 Frequency polygon showing the monthly income of families . . . 137
Fig. 2.52 Histogramwith polygon showing the average concentration
of SPM (mg/m3) in the air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Fig. 2.53 Histogram with polygon showing the monthly income
of families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Fig. 2.54 Frequency polygon of discrete variable (Distribution
of landslide occurrences) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Fig. 2.55 Frequency curve showing the average concentration
of SPM (mg/m3) in the air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Fig. 2.56 Frequency curve showing the monthly income of families . . . . . 141
Fig. 2.57 Types of frequency curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Fig. 2.58 Positive, negative and zero or no skewness . . . . . . . . . . . . . . . . . . 142
Fig. 2.59 Area under a standard normal curve . . . . . . . . . . . . . . . . . . . . . . . 145
Fig. 2.60 Degree of peakedness (Kurtosis) of frequency curve . . . . . . . . . . 149
Fig. 2.61 Cumulative frequency curve (Ogive) showing the average
concentration of SPM (mg/m3) in air . . . . . . . . . . . . . . . . . . . . . . . 151
Fig. 2.62 Cumulative frequency curve (Ogive) showing the monthly
income of families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Fig. 3.1 Vertical simple bar (Temporal change of urban population
in India since independence) Source Census of India, 2011 . . . . 157
Fig. 3.2 Horizontal simple bar (Total population in selected states
in India) Source Census of India, 2011 . . . . . . . . . . . . . . . . . . . . . 158
Fig. 3.3 Multiple bars showing the continent-wise urban population
(%) in 2000 and 2025*Source UN Population Division,
2009–2010 and The World Guide, 12th ed. * Projected
figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Fig. 3.4 Sub-divided bar (Production of different crops
in selected years in India) Source Ministry of Agriculture
and Economic Survey, 2010–2011 and Husain, 2014 . . . . . . . . . . 161
Fig. 3.5 Percentage bar showing the proportion of population
in different age groups in selected states in India Source
Census of India, 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Fig. 3.6 a Absolute population pyramid and b percentage
population pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Fig. 3.7 Ecological pyramid (Pyramid of numbers) . . . . . . . . . . . . . . . . . . 166
xxvi List of Figures
Fig. 3.8 Urban pyramid showing the percentage of towns
in different size classes in India . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Fig. 3.9 Rectangular diagram showing the area of irrigated land
(hectares) by different sources in India . . . . . . . . . . . . . . . . . . . . . 168
Fig. 3.10 Rectangular diagram showing the area of irrigated land
(%) by different sources in India . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Fig. 3.11 Triangular diagram (Geographical area of selected
biosphere reserves in India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Fig. 3.12 Square diagram (Population of selected million cities
of India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Fig. 3.13 Simple circular diagram (Cropping pattern in India, 2010–
2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Fig. 3.14 Pie diagram (Consumption of different fertilizers in India) . . . . . 175
Fig. 3.15 Percentage pie diagram showing the consumption
of different fertilizers in India . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Fig. 3.16 Doughnut diagram (Area under different land uses
in selected districts of West Bengal) . . . . . . . . . . . . . . . . . . . . . . . 180
Fig. 3.17 Steps of construction of cube diagram . . . . . . . . . . . . . . . . . . . . . . 183
Fig. 3.18 Cube diagram (Population of main seven tribes in India) . . . . . . 184
Fig. 3.19 Sphere diagram (Urban population of selected states
in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Fig. 3.20 Kite diagram showing the number of vegetation species
along the sand dune transect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Fig. 4.1 Plan of a college campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Fig. 4.2 Elements of a map (Source Sediment yield in global rivers,
Milliman and Meade 1983) . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 196
Fig. 4.3 World map of Ptolemy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Fig. 4.4 Location and extent of Dwipic world as conceived
in Ancient India [PURANAS] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Fig. 4.5 Relation between three surfaces of the earth . . . . . . . . . . . . . . . . . 205
Fig. 4.6 Geoid, sphere and ellipsoid (Source http://physics.nmsu.
edu/~jni/introgeophys/05_sea_surface_and_geoid/index.
html) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Fig. 4.7 Geoid and ellipsoid in the whole earth (Model of the earth’s
shape) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Fig. 4.8 Elements of an ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Fig. 4.9 Consideration of curvature of the earth in geodetic
surveying (after Kanetkar and Kulkarni 1984) . . . . . . . . . . . . . . . 209
Fig. 4.10 Equipotential surfaces as vertical datum [Relation
between orthometric height (H), ellipsoid or spheroid
height (h) and geoid height (N)] . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Fig. 4.11 Concept of datum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Fig. 4.12 Reduced level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Fig. 4.13 Geographic co-ordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Fig. 4.14 Cardinal points of the compass . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
List of Figures xxvii
Fig. 4.15 Concept of bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Fig. 4.16 True and magnetic meridian and true and magnetic bearing . . . . 217
Fig. 4.17 Whole circle bearing (a) and quadrantal bearing (b) . . . . . . . . . . 219
Fig. 4.18 Forward and backward bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Fig. 4.19 Magnetic declination (East and west magnetic declination) . . . . 221
Fig. 4.20 Magnetic inclination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Fig. 4.21 Open traverse (a) and closed traverse (b) . . . . . . . . . . . . . . . . . . . 224
Fig. 4.22 Locating a point by angular measurement (a)
and triangulation network (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Fig. 4.23 Locating a point by linear measurement (a) and trilateration
network (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Fig. 4.24 Layout, dimension and scale of million sheets and Indian
topographical maps (Old series) . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Fig. 4.25 Layout, dimension and scale of Indian topographical
maps (Open series) (National Map Policy-2005,
Projection-UTM, Datum-WGS-84) . . . . . . . . . . . . . . . . . . . . . . . . 236
Fig. 4.26 Hachure lines or contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Fig. 4.27 Relief shading or hill shading map . . . . . . . . . . . . . . . . . . . . . . . . 241
Fig. 4.28 Relation between contour spacing and steepness of slope . . . . . . 242
Fig. 4.29 Contour patterns of different relief features . . . . . . . . . . . . . . . . . 243
Fig. 4.30 Relation between contour pattern and topographic
expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Fig. 4.31 Trigonometrical station, benchmark and spot height . . . . . . . . . . 247
Fig. 4.32 a Bhola GTS tower near Singur and b Semaphore Tower,
Parbatichak, Arambagh, Hooghly, West Bengal, India . . . . . . . . . 248
Fig. 4.33 Form lines between contours to show minor topographic
details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Fig. 4.34 Simple chorochromatic map showing the spatial
distribution of forest-covered areas in West Bengal (Source
NATMO MAPS, DST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Fig. 4.35 Compound chorochromatic map showing the general land
use pattern of Denan village, Purba Medinipur, West
Bengal (Source Field survey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Fig. 4.36 Choroschematic map (Distribution of mineral and energy
resources in West Bengal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Fig. 4.37 a Population density map of West Bengal (2011), b
Cropping intensity map of West Bengal (2018–2019) . . . . . . . . . 262
Fig. 4.38 Visual difference between the Choropleth map (a)
and the Dasymetric map (b) (Dasymetric map shows
the exclusion areas of zero population) . . . . . . . . . . . . . . . . . . . . . 264
Fig. 4.39 Procedures of drawing of Isopleth map (Isotherms in this
sample area) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Fig. 4.40 Rainfall zones of West Bengal in Isopleth map (Source
NATMO MAPS, DST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
xxviii List of Figures
Fig. 4.41 Dot map showing the distribution of rural population
inWest Bengal (Source Primary census abstract and district
census report, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Fig. 4.42 Flow map showing the movement of local trains
between selected stations in West Bengal . . . . . . . . . . . . . . . . . . . 279
Fig. 4.43 Flow map showing the discharge of water in tributary
rivers and main river (River ‘I’) . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Fig. 4.44 Bar diagrammatic map showing the district-wise rural
population in West Bengal (Census 2011) . . . . . . . . . . . . . . . . . . . 283
Fig. 4.45 Circular diagrammatic map showing the gross cropped
area of different districts of West Bengal (2018–2019) . . . . . . . . 284
Fig. 4.46 Measurement of direction on map . . . . . . . . . . . . . . . . . . . . . . . . . 288
Fig. 4.47 Measurement of distance of curved features on map using
straight-line segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Fig. 4.48 Measurement of distance of curved features on map using
toned thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
Fig. 4.49 An Opisometer (a) and the technique of measurement
of distance of curved features on map using Opisometer (b) . . . . 291
Fig. 4.50 Measurement of area on map by Strips method . . . . . . . . . . . . . . 293
Fig. 4.51 Measurement of area on map by square grid method . . . . . . . . . . 295
Fig. 4.52 Measurement of area by dividing into regular geometric
shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Fig. 4.53 Measurement of area having irregular boundary using
geometric method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
Fig. 4.54 Principles of measurement of area using Simpson’s method . . . . 302
Fig. 4.55 Planimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
List of Tables
Table 1.1 Bi-variate data showing depth below ground (m) and air
temperature (°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Table 1.2 Nominal data (Number of male and female students
in different departments) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Table 1.3 Ordinal data (Literacy rate of few Indian states, 2011) . . . . . . . 21
Table 1.4 Moh’s scale of hardness of minerals (Ordinal scale) . . . . . . . . . 22
Table 1.5 Characteristics of different scales of measurement . . . . . . . . . . 24
Table 1.6 Geographical classification of data (Population densities
of some states in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Table 1.7 Chronological classification of data (Decadal growthrate
of population in India, 1901–2011) . . . . . . . . . . . . . . . . . . . . . . . 26
Table 1.8 Quantitative classification of data (Monthly income
of a group of people) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Table 1.9 Blank table to show season-wise water discharge
in Rupnarayan River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Table 1.10 Simple table (Population size of some selected countries,
2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Table 1.11 Complex table (Hypothetical state of the Earth’s
atmosphere) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Table 1.12 Simple frequency distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Table 1.13 Grouped frequency distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Table 1.14 Frequency distribution table (Based on the data
from Table 1.13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Table 1.15 Exclusive and inclusive methods of selection of class limit . . . 39
Table 1.16 Frequency distribution table showing the height
(in metre) from mean sea level . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Table 1.17 Frequency distribution table showing the mean monthly
temperature (°F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Table 1.18 Cumulative frequency distribution table using the data
of Table 1.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
xxix
xxx List of Tables
Table 1.19 Cumulative frequency distribution table using the data
of Table 1.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Table 1.20 Tabular presentation of data (% of sand, silt and clay
in bed sediments of Rupnarayan River) . . . . . . . . . . . . . . . . . . . 44
Table 2.1 Types of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Table 2.2 Data for line graph or historigram (Temporal change
of total population in Kolkata Urban Agglomeration) . . . . . . . . 59
Table 2.3 Data for line graph or historigram (Production of rice
in India, 2000–2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Table 2.4 Database for arithmetic and logarithmic line graph (Age
and sex-specific variation of death rates) . . . . . . . . . . . . . . . . . . 62
Table 2.5 Worksheet for poly graph (Total, male and female literacy
rates in different census years in India) . . . . . . . . . . . . . . . . . . . . 66
Table 2.6 Worksheet for band graph (Production of different crops
in India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Table 2.7 Monthly wet-bulb temperature (°F) and relative humidity
(%) of Kolkata, West Bengal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Table 2.8 Mean monthly temperature and rainfall of Burdwan
district, West Bengal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Table 2.9 Database for ternary graph (Proportion of sand–silt-clay
in sediments) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Table 2.10 Data for radar graph (Production of different crops
in different years) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Table 2.11 Percentage of days wind blowing from different directions . . . 82
Table 2.12 Data for polar graph (The orientation of corries
in a glacial region) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Table 2.13 Database for scatter graph (The distributions of air
temperature in the month of April around an urban area) . . . . . 83
Table 2.14 Data for ergograph (Monthly temperature, relative
humidity and rainfall of Howrah, West Bengal) . . . . . . . . . . . . . 86
Table 2.15 Data for ergograph (Net acreage of different crops
and their growing seasons of Howrah, West Bengal) . . . . . . . . . 88
Table 2.16 Database for circular ergograph (Rhythmic seasonal
activities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Table 2.17 Data for ombrothermic graph (Average temperature
and rainfall of Purulia district, West Bengal) . . . . . . . . . . . . . . . 90
Table 2.18 Water need and supply (mm) of a region (field capacity:
100 mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Table 2.19 Water budget estimation for a sample study area
(elevation: 12 m; field capacity: 102 mm) . . . . . . . . . . . . . . . . . . 95
Table 2.20 Stream stage and discharge relationship . . . . . . . . . . . . . . . . . . . 102
Table 2.21 Worksheet for Lorenz curve (The number and area
of land holdings) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Table 2.22 Worksheet for Lorenz curve (Total and urban population
of six North Bengal districts of West Bengal) . . . . . . . . . . . . . . 108
List of Tables xxxi
Table 2.23 Inequality in the distribution of income of people
of Sweden, USA and India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Table 2.24 Calculations for rainfall dispersion graph (Annual rainfall
of Bankura district, year 1976–2015) . . . . . . . . . . . . . . . . . . . . . 115
Table 2.25 Rank-size relationship of Indian cities (according to G.K.
Zipf method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Table 2.26 Rank-size relationship of Indian cities (according
to Pareto method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Table 2.27 Expected populations and their deviations from actual
populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Table 2.28 Calculations for area–height graph and hypsometric
curve in a sample drainage basin (Fig. 2.44) . . . . . . . . . . . . . . . 128
Table 2.29 Grouped frequency distribution with equal class size
(average concentration of SPM in the air) . . . . . . . . . . . . . . . . . 134
Table 2.30 Grouped frequency distribution with unequal class size
(monthly income of families) . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Table 2.31 Methods of calculating Y in f (x) for constructing
a normal curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Table 2.32 Standard normal distribution table . . . . . . . . . . . . . . . . . . . . . . . 147
Table 2.33 Worksheet for drawing Ogive (with equal class size) . . . . . . . . 150
Table 2.34 Worksheet for drawing Ogive (with unequal class size) . . . . . . 150
Table 3.1 Types of diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Table 3.2 Data for vertical simple bar diagram (Temporal changes
of urban population in India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Table 3.3 Data for horizontal simple bar diagram (Total population
in selected states in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . 159
Table 3.4 Calculations for multiple bar diagram (Continent-wise
urban population) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Table 3.5 Calculations for sub-divided bar diagram (Production
of different crops in India, 1950–1951 to 2010–2011) . . . . . . . . 161
Table 3.6 Calculations for percentage bar diagram (Proportion
of population in different age groups in selected states
in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Table 3.7 Worksheet for age-sex pyramid (Based on the population
of Purba Medinipur district, West Bengal, 2011) . . . . . . . . . . . . 165
Table 3.8 Database for urban pyramid (Size class distribution
of towns in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 167
Table 3.9 Calculations for rectangular diagram (Area of irrigated
land by different sources of irrigation in India) . . . . . . . . . . . . . 169
Table 3.10 Worksheet for triangular diagram (Geographical area
of selected biosphere reserves in India) . . . . . . . . . . . . . . . . . . . 171
Table 3.11 Worksheet for square diagram (Population of selected
million cities of India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Table 3.12 Worksheet for simple circular diagram (Cropping pattern
in India, 2010–2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
xxxii List of Tables
Table 3.13 Worksheet for pie-diagram (Consumption of fertilizers
in India, lakh tonnes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Table 3.14 Database for doughnut diagram (Area under different
land uses in selected districts of West Bengal) . . . . . . . . . . . . . . 180
Table 3.15 Worksheet for cube diagram (Population of main seven
tribes in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Table 3.16 Worksheet for sphere diagram (Urban population
in selected states in India, 2011) . . . . . . . . . . . . . . . . . . . . . . . . . 186
Table 3.17 Data for pictograms (Production of wheat in different
years in India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Table 3.18 Database for kite diagram (Number of vegetation species
along the sand dune transects) . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Table 4.1 Relation between colatitude (polar angle) and latitude . . . . . . . 213
Table 4.2 Suitable projections for different maps . . . . . . . . . . . . . . . . . . . . 216
Table 4.3 Methods of conversion of Q. B. from W. C. B . . . . . . . . . . . . . . 220
Table 4.4 Types of maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Table 4.5 Layout, dimension and scale of million sheets and Indian
topographical maps (Old series) . . . . . . . . . . . . . . . . . . . . . . . . . 235
Table 4.6 Layout, dimension and scale of open series maps
(National Map Policy-2005, Projection-UTM,
Datum-WGS84) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Table 4.7 Contour patterns of typical topographic features . . . . . . . . . . . . 244
Table 4.8 Worksheet for choropleth map (Population density
of different districts of West Bengal, 2011 census) . . . . . . . . . . 261
Table 4.9 Category-wise population density in different districts
in West Bengal (2011 census) . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Table 4.10 Worksheet for cropping intensity map of West Bengal
(2018–2019) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Table 4.11 Category-wise cropping intensity in different districts
in West Bengal (2018–2019) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Table 4.12 Calculations for dot map (Status of rural population
in different districts of West Bengal, census 2011) . . . . . . . . . . 275
Table 4.13 Worksheet for flow map (Number of local trains
connecting between selected stations in West Bengal,
India) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Table 4.14 Worksheet for computing flow of water in tributary rivers
and main river ‘I’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Table 4.15 Calculations for bar diagrammatic map (District-wise
rural population in West Bengal, census 2011) . . . . . . . . . . . . . 285
Table 4.16 Calculations for circular diagrammatic map (Gross
cropped area of different districts of West Bengal, 2018–
2019) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Table 4.17 Methods of measurement of area on map . . . . . . . . . . . . . . . . . . 292
Chapter 1
Concept, Types, Collection, Classification
and Representation of Geographical Data
Abstract Geography is a scientific discipline which emphasizes on the collection,
processing, suitable representation and logical and scientific interpretation of various
types of primary and secondary data for better understanding and explanation of the
spatial distributions and variations of different geographical features and phenomena
on or near the surface of the earth. This chapter focuses on the concept and types
of data used in geographical analysis, sources of each type of data, methods of their
collection as well as the advantages and disadvantages of their use. Major differ-
ences between various types of data are discussed clearly with suitable examples.
It includes the detailed discussion of the concept of attribute and variable, types of
variables and differences between them. Different types of measurement scales used
in geographical analysis, their characteristics and application in geographical study
have been explained with numerous examples. Techniques of classification, tabula-
tion and processing of the collected data on different basis (i.e. based on location, time
etc.) are discussed properly with special emphasis on the preparation of frequency
distribution table and related terminologies. Methods of representation of all types
of geographical data, their appropriateness and advantages and disadvantages have
been explained with suitable examples.
Keywords Geographical data · Primary data · Secondary data · Data collection ·
Measurement scale · Data processing · Data representation
1.1 Introduction
Geography is a scientific discipline in which various types of primary and secondary
data are used voluminously to explain and analyse different geographical events and
phenomena. Collected data are organized, represented and interpreted logically and
scientifically using various techniques for better understanding and explanation of
the spatial distributions and variations of different geographical features on or near
the surface of the earth.Geographical data needs appropriate, systematic and logical
presentation for better understanding of their cartographic characteristics. Suitable,
accurate and lucid demonstration and visualization of geographical data becomes
helpful for their correct analysis, explanation and realization.
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2 1 Concept, Types, Collection, Classification …
Geographical studies emphasize how and why different features vary from one
place to another and how spatial patterns of these features change with time. Geogra-
phers always begin with the question ‘Where?’, investigating how different features
are located on a physical or cultural area, monitoring the spatial patterns and the
variations of features. Modern geographical study has shifted to ‘Why?’, specifying
why a particular spatial pattern exists, what kinds of processes (spatial or ecolog-
ical) have influenced the pattern, as well as why such processes operate. Graphical
visualization of various geographical data is the key to realize the nature and char-
acter of data, the pattern of their spatial and temporal variations, communicating
the knowledge of spatial information, to classify different features and objects and
understanding their relationships, formulation of principles which become helpful
for proper understanding of the real world.
Graphs, diagrams and maps are three important methods of visual representation
of data in geography. These three methods are unique and distinctive in terms of the
principles and procedures followed and applied for their depiction. In narrow sense,
graphical representation means portraying of datausing various types of graphs but
in broader geographical perspective, all types of graphs, diagrams andmapping tech-
niques are considered as graphical methods of presentation of data. Different graph-
ical techniques (graphs, diagrams andmaps) are very popular to the geographers and
researchers as they help for better understanding of the world around us by enriching
spatial intelligence and capacity of human beings for technical and logical decision-
making. Graphical representation of geographical data is very simple, attractive and
easily recognizable not only to the geographers or efficient academicians but also to
the common literate people.
1.2 Concept of Data
A body of information in numerical form is known as data. In other words, data
are characteristics or information which are generally numerical in nature and are
collected through observation. In technical sense, data means a set of values in
quantitative or qualitative form concerning one or more individuals or objects. Data
contain some facts and information from which an inference may be made or a
reliable conclusion may be drawn. Actually, data are the raw materials of any type
of research or investigation. So, the collection of reliable and dependable data is
the prerequisite condition for conducting any research or investigation and drawing
consistent conclusions.
For instance, if we want to analyse the trends and patterns of rainfall distribution
and its changes over time of any region, at first daily or monthly rainfall data (in
numeric figure) should be collected and then suitable techniques should be applied
on those collected data for drawing reliable inferences.
Major characteristics of data are:
1. Data must be represented in numerical forms.
1.2 Concept of Data 3
2. All the data must be interrelated with each other.
3. They must be meaningful to the purpose for which they are required.
1.3 Concept of Geographical Data
Data that record the locations and characteristics of natural or human features or
activities which occur on or near the earth’s surface are called geographical data.
Two important characteristics of these data are—i) the reference to geographic space
or earth surface (expressed by geographical co-ordinates) and ii) the representation
at specific geographic scale.
Example Amount of rainfall, temperature, height from mean sea level, number
of landslide occurrences, volume of water discharge in river, number of popula-
tion, density of population, production of agricultural crops etc. are considered as
geographical data as they possess the above mentioned two characteristics.
Geographers and researchers use huge amount of statistical information and data
for proper and logical understanding and explanation of various geographical features
and phenomena on or near the earth’s surface. Different statistical techniques and
principles are widely used by them for the correct and scientific processing, analysis,
depiction and interpretation of the collected data.
1.4 Types of Data (Geographical Data)
Like other data, geographical data are also of two main types on the basis of their
nature and characteristics:
1.4.1 Qualitative Data (Attribute)
The qualitative characteristic of the information which can’t be measured and
expressed in numerical or quantitative terms is called qualitative data or attribute.
Attribute refers to the characteristics of the quality of an observation which can be
observed, ascertained and classified under different categories but can’t be expressed
in quantitative or numerical forms. There are numerous qualitative data which are
used in geographical study.
For example, skin colour of the people, educational status, efficiency, caste system,
attitude and mentality of people etc. are this type of data. All the qualitative data are
converted into numerical or quantitative data for efficient and successful application
of statistical techniques during geographical investigation. For instance, 100 people
are literate, 150 people are of general caste, skin colour of 340 people is black etc.
4 1 Concept, Types, Collection, Classification …
In all those cases, the quality or characteristics of the data has been converted into
numeric forms.
1.4.2 Quantitative Data (Variable)
The characteristic of the information which can be measured and expressed numeri-
cally or quantitatively in suitable units is called quantitative data or variable. Variable
refers to the quantitative characteristic of an individual or item which takes different
values depending on situation and place and these values can always be measured.
The variable whose values depends on chance and can’t be predicted is called random
variable.
For example, average monthly rainfall is 15 cm, number of first order streams in
the river basin is 345, average volume of water discharge in the stream is 560 m3/sec,
rate of soil erosion is 1mm/year, production of rice is 1200 kg/acre, literacy rate of the
country is 65%, fertility rate of any country is 12 persons/year/1000 peoples etc. are
the quantitative expression of data. These data are more suitable for the application
of statistical techniques and successfully used in geographical analysis.
1.4.2.1 Continuous Variable and Discontinuous or Discrete Variable
The variable which can take any value within a specified range is called continuous
variable. These variables can be expressed not only in integral part, but also in
fraction of any part, however small it may be. When the continuous variables are
represented in the form of a series, then it is known as continuous series.
Example Amount of rainfall, temperature, height from sea level, velocity of river
water, literacy rate, weight of people etc. are the examples of continuous variables.
The amount of rainfall may be 25 cm or 25.5 cm or 25.55 cm or any other values.
Similarly, the literacy rate may be 68% or 68.25% or 68.59% or any other values.
The variable which can assume only some isolated values or integral values is
called discontinuous or discrete variable. Discrete variables can’t be expressed in
fractional values. When the discontinuous or discrete variables are expressed in the
form of a series, then it is called discontinuous or discrete series.
Example The number of streams in different orders in a river basin, number of
household in a village, number of agricultural or industrial workers in a country,
number of peoples affected by flood hazard, number of migrated peoples etc. are the
examples of discrete variables. The number of household in a village may be 205 or
206. But, it can’t be 205.65 as a household can’t be divided into parts or fractions.
Similarly, the number of people affected by flood hazard may be 450 or 451, but it
can’t be 450.5 or 450.75.
1.4 Types of Data (Geographical Data) 5
1.4.2.2 Difference Between Continuous and Discontinuous or Discrete
Variables
Major differences between continuous and discontinuous or discrete variables are as
follows:
Continuous variable Discontinuous or discrete variable
1. These variables can take any value within a
specified interval
1. These variables can take only some isolated or
integral values
2. Can be expressed not only in integral part,
but also in fraction
2. Can be expressed only in whole numbers,
fractional expression is not possible
3. These variables are measurable but not
countable
3. These variables are countable but not
measurable
4. Continuity of representation of variables is
maintained
4. Continuity of representation of variables is not
maintained
5. Variables are expressed by a range, like ∞
≤ X ≤ ∞
5. Variables are expressed by a fixed value, like
X = 0, 8, 12, 15, etc
6. Example: Height, rainfall, temperature,
velocity etc.
6. Example: Number of households, number of
students, number of accidents etc.
1.4.3 Uni-Variate Data and Bi-Variate Data
Statistical data relating to themeasurement of one variable only are called uni-variate
data. For example, amount of organic matter in soil, concentration of SuspendedParticulate Matter (SPM) in air, annual production of rice, income of a family etc.
Generally, central tendency, dispersion, skewness and kurtosis etc. are used as the
statistical measurements of these variables. Uni-variate data are represented by a
letter or symbol ‘x’ and the ‘n’ number of values of ‘x’ variable are expressed by
x1, x2, x3, x4, . . . . . . . . . . . . . . . xn.
Data relating to the simultaneous measurement of two variables are called bi-
variate data (Table 1.1). For example, height from mean sea level and number of
settlements, volume of surface run-off and rate of soil erosion, income and expendi-
ture of a family, amount of fertilizer used and crop production, distance from Central
Business District (CBD) and lower atmospheric temperature etc. Here, one variable
is influenced by another variable and thus bi-variate data has an independent and
a dependent variable. Co-relation and regression are popular statistical techniques
for the analysis of these variables. Bi-variate data are represented by two letters
or symbols (xi, yi) and the ‘n’ pairs of values are expressed by (x1, y1), (x2, y2),
(x3, y3)………. (xn, yn).
6 1 Concept, Types, Collection, Classification …
Table 1.1 Bi-variate data showing depth below ground (m) and air temperature (°C)
Sl. No Depth below
ground (m)
Air temperature
(°C)
Sl. No Depth below
ground (m)
Air temperature
(°C)
1 0 10.6 9 840 22.1
2 140 11.6 10 690 22.6
3 300 13.3 11 590 23.6
4 170 13.8 12 820 25.5
5 310 15.1 13 1020 26.9
6 340 17.0 14 1150 30.2
7 460 19.3 15 970 30.6
8 550 20.6 16 830 26.2
1.4.4 Difference Between Uni-Variate Data and Bi-Variate
Data
Major differences between uni-variate and bi-variate data are as follows-
Uni-variate data Bi-variate data
1. The word ‘Uni’ means one. Statistical data
involving one or single variable is called
uni-variate data
1. The word ‘Bi’ means two. Statistical data
involving two variables (one independent and
one dependent variable) is called bi-variate data
2. It is not associated with causes or
relationships
2. It is closely associated with causes or
relationships
3. Description of a specific variable is the main
purpose of uni-variate analysis
3. Explanation is the main purpose of bi-variate
analysis
4. Central tendency (mean, median and mode),
dispersion (range, quartile, mean deviation,
variance and standard deviation), skewness and
kurtosis are the main techniques of uni-variate
analysis
4. It uses different techniques like co-relations,
regression, comparisons, causes and
explanations etc. for the analysis of two
variables simultaneously
5. The result of uni-variate analysis is shown in
bar graph, pie-chart, line graph, box and
whisker plot etc.
5. The result of bi-variate analysis is shown in
table where one variable is contingent on the
values of the other variable
6. Example: Annual production of rice, annual
precipitation, amount of suspended particulate
matter in air etc.
6. Example: Relation between height from
mean sea level and number of settlements,
volume of surface run-off and rate of soil
erosion, distance from Central Business
District and temperature etc.
1.4 Types of Data (Geographical Data) 7
1.4.5 Independent Variable and Dependent Variable
The variable which stands alone and does not depend on other variables, moreover
controls other variables is called independent variable. Independent variables may
be one or more in number. This variable is expressed by ‘x’ and is shown along
‘X’-axis in graph.
The variable which depends on other variables and is affected by them is called
dependent variable. The value of dependent variable undergoes changes due to the
change of value of independent variables. This variable is expressed by ‘y’ and is
shown along ‘Y’-axis in graph.
Example In the above data (Table 1.1), air temperature changes with the change
of depth below ground. So, the air temperature is dependent variable and the depth
below ground is independent variable. Again, the production of agricultural crops
depends on availability of water, amount of fertilizer used, labour used etc. Here,
crop production is dependent variable but availability of water, amount of fertilizer
used, labour used are independent variables.
1.4.6 Difference Between Qualitative Data (Attribute)
and Quantitative Data (Variable)
The following are the differences between qualitative and quantitative data:
Qualitative data (Attribute) Quantitative data (Variable)
1. Data representing the qualitative
characteristics of the statistical information
1. Data representing the quantitative
characteristics of the statistical information
2. Data can be observed, ascertained and
classified under different categories but can’t
be expressed in numerical form
2. Data attain different values which can easily
be measured and expressed in numerical form
3. Data should be transformed into quantitative
forms before used in statistical analysis
3. Different statistical techniques can easily be
applied on those data
4. Example: Educational status, caste system,
attitude etc.
4. Example: Amount of rainfall, volume of
water discharge, rate of sediment transport etc.
On the basis of sources of collection, geographical data are of two types.
1.4.7 Primary Data
Primary data are those data which are collected for a specific purpose directly from
the field of investigation, and hence are original in nature. These types of data are
collected originally by the individual, group or authority who requires the data for
their own use and treatment. These data have not been used in quantitative research
previously. These are called raw data or basic data as they are directly collected from
8 1 Concept, Types, Collection, Classification …
the field by the field-workers, investigators and enumerators. The level of accuracy
and reliability of these data depend on the knowledge, efficiency, consciousness and
mentality of the researcher or investigator and also on the methods of data collection.
The places or sources from which primary data are collected are known as primary
sources.
Examples The data collected from measurements of river depth, width, water
velocity, water discharge, tidal water level etc. directly in the field by the researcher
using various instruments are primary data. Similarly, various socio-economic data
(caste, religion, literacy rate, job opportunity, income, expenditure, marital status,
immunization status etc.) collected from household survey using survey schedule by
the researcher are the examples of primary data.
1.4.8 Secondary Data
The data which have previously been collected and published by someone for one
purpose but subsequently treated and utilized by another one in a different connection
are called secondary data. Secondary data are actually collected and published by the
organizations other than the authorities who need them subsequently for their use.
So, primary data of one organization become the secondary data of other organization
who later want to use those data. Because of this, secondary data are not considered
as basic data. The sources from which secondary data are collected are known as
secondary sources.
Examples Data, collected from any published books and journals, from different
maps, from internet sources, from different government and non-government offices
are the examples of secondary data. The Statistical Abstract of India and Monthly
Abstract of Statistics, published by Central Statistical Organization and other
publications of Government are different sources of secondary data.
1.4.9 Advantages of Use of Primary Data Over the Secondary
Data
There is no hard and fast rule about which data should be used in geographical
research or investigation. The nature, scope and purpose of the geographical enquiry
should be taken into consideration whether primary data should be used or secondary
data are to be utilized. Though the utilization of secondary data is more convenient
and economical, but the use of primary data is preferableandmuch safer from several
standpoints:
(a) Primary data usually show more detailed information and a description of the
investigation along with the unit of measurement.
1.4 Types of Data (Geographical Data) 9
(b) The methods, sources and any approximations used for the collection of data
are clearly and specifically mentioned in those data. So, it can be decided in
advance how much reliance can be given on those data while they are being
used.
(c) Primary data are more reliable, authentic and accurate than secondary data as
the later contain errors because of transcription, rounding etc.
Inspite of this, the secondary data are used due to the following reasons:
(a) Primary data are not available or can’t be collected directly due to limitations
of time and money during data collection.
(b) To compare the data collected over a long period of time, the use of secondary
data is required. Utmost accuracy is not so much necessary in these cases.
1.4.10 Difference Between Primary and Secondary Data
Actually, primary data and secondary data are same because the former is trans-
formed into the later with the advancement of time. The major differences between
primary and secondary data are:
Primary data Secondary data
1. Primary data are collected directly from
the field or area under study by the
investigator
1. Secondary data are collected from any
published books or journals, offices, internet
sources, institutions etc.
2. Data are the result of direct observations
and interactions in the study area
2. Data are mainly the result of publications
3. Trained and efficient manpower is needed
during the collection of primary data
3. Trained and efficient manpower is not essential
for the collection of data. Non-trained person can
collect the data
4. Quality of data is largely affected by the
knowledge, efficiency, consciousness and
mentality of the investigator
4. Researcher or investigator has no role to
control the quality of data
5. Data are more accurate, authentic and
reliable
5. Data are less reliable due to the possibility to
be erroneous
6. Data are always collected in original unit 6. Data can be collected in original unit or in any
other converted unit, like aggregate, ratio,
average, percentage etc.
7. Collection of data is time consuming,
costly and sometimes becomes risky
7. Data collection is less time consuming and cost
effective
8. These data are at the first stage of their
utilization and numerical techniques are not
applied previously
8. Different numerical techniques have been
applied previously in those data, i.e. they are in
second, third or any other stages of their
utilization
9. Primary data is preferred more by the
researchers in statistical investigations
because of its several advantages
9. Secondary data is used in those cases when
primary data is unavailable or can’t be collected
directly
10 1 Concept, Types, Collection, Classification …
1.5 Methods of Data Collection
There is no hard and fast rule in adopting a specific method for the collection of
geographical data. The method of data collection is decided by the objectives and
purposes of the study. Young (1994) has divided the data sources into two classes: (a)
field sources and (b) documentary sources. Field sources are the sources of primary
data whereas the documentary sources are the sources of secondary data.
1.5.1 Methods of Primary Data Collection
Generally, five methods are followed for the collection of primary data:
1. Observation method
2. Interview method
3. Sampling method
4. Experimentation method
5. Local sources method.
1.5.1.1 Observation Method
Continuous and intensive observation of different objects, events or phenomena is
an important method of primary data collection. The success of this method depends
on the knowledge, efficiency and capability of the researcher or investigator. There
are three types of observations:
Direct Observation Method
The researcher or investigator collects the necessary information directly by himself
or herself beingpresent in thefield. The researcher visits the area to be studied keeping
some hypotheses in his/her mind. After intensive and careful field observation, some
new ideas and experiences are added to the previous hypotheseswhich help to develop
the theory and make the collected primary data reliable and relevant.
Example In case of landslide study, the researcher or investigator directly visits the
land slide affected area and collects different data regarding the total area affected
by land slide, volume of materials displaced, length of sliding, slope of the land,
composition of materials etc.
Advantages and Disadvantages of Direct Observation Method
Advantages
(i) More reliable and accurate data can be collected without any biasness.
(ii) Usable for small area investigation.
1.5 Methods of Data Collection 11
(iii) Privacy of data can be maintained.
(iv) Clarity and homogeneity of data can be maintained.
(v) Collection of complete data is possible.
Disadvantages
(i) Probability of wastage of time and money.
(ii) Method can’t be applied in large study area.
(iii) Sometimes, the self-feelings, emotions, mentality and prejudices of the
researcher affect the collection method and quality of the data.
(iv) Sometimes, the data collection becomes risky.
Indirect Observation Method
When the responder is not agreeing to provide information or to answer the questions
accurately, then this method is applied. In this situation, the responder is avoided and
information is collected from the associated third person. Data is collected by the
researcher himself or herself or by the enumerator appointed by the researcher.
Advantages and Disadvantages of Indirect Observation Method
Advantages
(i) Less time consuming and cost effective.
(ii) Effective for the collection of qualitative data.
(iii) Data can be collected in risky condition.
(iv) Effective for data collection in large population.
(v) Unbiased data collection is possible.
Disadvantages
(i) The data are not as reliable as collected from the associated third person.
(ii) Information provider may be biased.
(iii) Data may be biased due to negligence of information provider.
(iv) Collected data may be erroneous due to lack of trained enumerator.
Participation Observation
The researcher or investigator collects the information by staying, living and inter-
acting with the people of the area under study. In this method, the researcher makes
a close and intricate relationship with the local people of the area and observes their
daily activities and life style intensively.Questions are not asked to the people but data
are collected by observations, feelings and individual judgements of the investigator.
Example For the intensive study of the livelihood pattern and social adjustments of
the people of any indigenous tribal society, the researcher or investigator live and
makes a close relationship with the people of the society for collecting required
information for the fulfilment of the purpose.
12 1 Concept, Types, Collection, Classification …
Advantages and disadvantages of participation method
Advantages
(i) Reliable, unbiased and accurate data are collected as the researcher collects
the data by making close relation with the local people.
(ii) Simple, easy and unambiguous technique of data collection.
(iii) Effective in qualitative data collection.
(iv) Collection of data about any specific group of people becomes possible.
(v) Researcher can change and modify the hypothesis of research easily.
Disadvantages
(i) Complete observation and understanding about the research area is difficult
as it is totally unknown to the researcher.
(ii) It is a valiant and risky method for data collection.
(iii) Time consuming and costly because the researchers have to stay in the research
area for a certain period of time.
(iv) Prior experience and training is required for the collection of data.
(v) Limited applicability in large research area.
1.5.1.2 Interview MethodIn interview method, information is collected by the conversation between investi-
gator or enumerator (interviewer) and the informant (interviewee). The interviewer
makes a close interaction and face-to-face discussionwith the informant for collecting
the data. Interview methods are of three types.
Interviewing by Questionnaire Method
In thismethod, the enumerators interview the concerned persons directly or indirectly
and ask questions to collect information. The information is gathered generally on
standard set of questions. Before collecting the data, a standard questionnaire is
prepared by the researcher.
Example If a researcher wants to study the impact and management of flood in
any flood-prone area, he/she will prepare a standard questionnaire considering the
following points, like causes of flood, frequency of flood, duration of water logging
during flood, area affected by flood, problems of flood, sources of food and drinking
water during flood, flood controlling measures taken by governmental and non-
governmental agencies, precautions to avoid flood, any advantages from flood etc.
Characteristics of Standard Questionnaire
(a) The questions should be meaningful, concise, clear and easy to understand to
the interviewee.
1.5 Methods of Data Collection 13
(b) The number of questions should be limited and they will be arranged
sequentially and systematically.
(c) Questions should be impartial and unbiased to avoid the hesitation of the
interviewee.
(d) All the questions should be relevant and will be sufficient for the fulfilment of
the purpose of the research.
(e) Questions should be free of religious, political and other prejudices.
(f) Calculative questions should be avoided.
Questionnaire method is of two types.
Direct Questionnaire Method
In this method, the researchers or the enumerators appointed by the researcher go
personally to the persons or to the sources fromwhom (which) the information should
be collected. The enumerators interview the concerned persons and ask the questions
directly (face to face) during the time of data collection. This method is also called
interview schedule method.
Advantages and disadvantages of Direct Questionnaire method
Advantages
(i) Data confirm high degree of accuracy as the investigators or enumerators have
direct contact with the people (interviewee).
(ii) Data are more reliable and dependable.
(iii) The purpose of the study and the meaning of each question can clearly and
patiently be explained to the interviewee.
(iv) It helps to collect the relevant information only.
(v) Privacy of data will be maintained.
(vi) Testing of data accuracy is possible.
Disadvantages
(i) It is very expensive, time consuming and complex technique of data collection.
(ii) Difficult to apply for large observations in extensive area.
(iii) Untrained and inefficient enumerator may collect erroneous information.
(iv) It allows the personal prejudices of the enumerators or the investigators to
affect the quality of the data and the inferences to be drawn.
Postal Method of Questionnaire Survey
A standard questionnaire is prepared and sent to different addresses by post for
answering the questions. Generally, all the questionnaires are accompanied by a
letter of explanation and self-addressed envelopes in order to receive the information
properly at the earliest. This method is widely used for data collection in planning
process.
14 1 Concept, Types, Collection, Classification …
Advantages and disadvantages of Postal Questionnaire method
Advantages
(i) Thismethod helps extensive investigations and covers the large fields of study.
(ii) It is a very easy and quick method. Data can be collected within very short
time.
(iii) It is cost effective for data collection. Only postal charges are required.
(iv) It is free from personal bias of the enumerators or investigators.
(v) Data can be easily collected from long distances.
(vi) Very useful to judge the national point of view.
Disadvantages
(i) Someof thequestionnairesmaynot be answered and returned to the researcher.
(ii) Questionnairesmaybe returned to the researcherwithout giving proper answer
and filled in. Wrong answer may be given without understanding proper
meaning of the questions.
(iii) Method can’t be applied to the informantswho are illiterate orwho are ignorant
about the importance and requirement of the information.
(iv) The accuracy of the information can’t be verified. So, data are not so much
reliable and dependable.
Interviewing by Informal Method
In this method, the researcher or investigator collects the required information out of
the inadvertence of the informants.Generally, thismethod is applied for the collection
of information about any specific phenomenon or event.When the informants are not
agreeing or hesitating to provide sufficient information, then the investigator attempt
to collect necessary information by immaterial and superfluous discussion with the
informants. The informants explain the actual fact unintentionally to the investigator
which becomes important information to the researcher. No questionnaire is needed
for collecting data by this method. The researcher or investigator collects the data by
asking the questions to the informants from his/her memory.
Example For conducting a study about the dimension and status of illegal coal
mining in any region, the researcher needs to collect information regarding the area
and number of illegal coal mines, number of people engaged in this work, amount of
daily coal withdrawal, means of mining, major uses of the mined coal, any problems
faced by the miners etc.
Advantages and disadvantages of Informal interview method
Advantages
(i) Easy data collection by this method by the extrovert persons.
(ii) Qualitative data can easily be collected by this method.
(iii) Collected data are more reliable and dependable.
(iv) Behaviour of the informants is expressed accurately.
1.5 Methods of Data Collection 15
Disadvantages
(i) Trained and efficient investigator is required.
(ii) Consciousness of the enumerator or investigator is essential.
(iii) Very costly and time consuming.
Interviewing by Telephone
The researcher collects the information by telephonic interview of the informants.
When enormous information is needed urgently within very short time, then this
method is followed.
Advantages and disadvantages of Telephone interview method
Advantages
(i) Collection of huge information within very short time and spending little
money.
(ii) Lesser number of investigators is needed.
(iii) Data are reliable and collected systematically.
(iv) Very suitable to apply in small research area.
Disadvantages
(i) Applicability of this method depends on the availability of telephonic commu-
nication.
(ii) Informants are not always available in urgent condition.
1.5.1.3 Sampling Method
Sampling is a very importantmethod for the collection of different primary data. Reli-
able statistical inferences can easily be drawn about a large number of observations
(population) under study by testing small samples collected from the population.
The members of the population which are selected for statistical testing are called
samples and the technique of sample selection is called sampling. Sampling tech-
nique is used very popularly and significantly for the collection of data to be used in
different geographical study and research.
Example For assessing the quality of water of a lake, required number of water
samples should be collected from different parts and depths of the lake.
Similarly, the socio-economic status of the people of a large slum area should be
studied by collecting required data from the slum households. When the collection
of data from all slum households is not possible due to time and money constraint,
then slum households should be selected by suitable sampling method.
16 1 Concept, Types, Collection, Classification …
Advantages and Disadvantages of Sampling Method
Advantages
(i) Data collectionis cost effective and less time consuming.
(ii) It is applicable for all types of geographical survey.
(iii) Minimum number of investigators is required.
(iv) All the factors regarding survey and data collection can bemonitored carefully.
(v) Trained and efficient researcher can solve different critical problems by
collecting data in this method.
Disadvantages
(i) Collection of data by sampling technique requires trained and efficient
enumerator or investigator.
(ii) Presumptions, prejudices, partiality and negligence of the enumerator or
investigator will affect the selection of samples.
(iii) Wrong sampling technique or collection of wrong samples makes the result
erroneous and less applicable.
(iv) Results from sample study may not always reflect all the characteristics of the
whole population.
1.5.1.4 Experimentation Method
It is an important part of the sampling method for primary data collection. In this
method, the researcher or investigator collects the required samples from the study
area, analyse and test the collected samples in the laboratory or research centre and
generates numerous primary data.
Example For knowing the mineral composition of soils of any region, we have to
collect the required number of soil samples from the concerned study area, and then
the collected samples should be tested and experimented in the laboratory using
different instruments (preferably using X-Ray Diffraction technique) and chemicals.
Similarly, if we want to know about the arsenic contamination of groundwater of
any region, then sufficient numbers of groundwater samples should be collected from
wells, tube-wells or any other sources for testing them in the laboratory to generate
primary data.
Advantages and Disadvantages of Experimental Method
Advantages
(i) It is an ideal method for generating data in the laboratory.
(ii) Numerous data can be generated within very short time.
(iii) All types of variables can be controlled and monitored easily.
(iv) It needs minimum number of enumerator or investigator.
Disadvantages
(i) Generation of data in this method is very costly.
1.5 Methods of Data Collection 17
(ii) It can’t be applied in all types of geographical research.
(iii) Trained and efficient investigators are required for the utilization of different
instruments and peripherals in the laboratory.
1.5.1.5 Local Sources Method
The researcher or any institution appoints the local people of the research area as the
enumerator or investigator for collecting data about any geographical phenomenon
or event. Being local residents, the enumerator comprise clear-cut and explicit idea
about the study area. They collect all the required information by direct observations
about any phenomena and send the collected data to the concerned researcher or
institution. Generally, different types of regional geographical data are collected by
this method.
Example Measurement of daily water discharge of a stream, measurement of hourly
tidal water level in a tidal river, collection of weather-related data (atmospheric
temperature, amount of rainfall, wind direction, wind velocity, air pressure, humidity
etc.) at any weather station should be done by appointing the local residents as the
investigator.
In socio-economic survey, the study of daily livelihood pattern of a particular
group of people can be made following this method.
Advantages and Disadvantages of Local Sources Method
Advantages
(i) Data can be collected continuously and instantly.
(ii) Fewer enumerators can collect the required data.
(iii) Decision can be made quickly.
(iv) Place-wise data can be collected from an extensively large research area.
Disadvantages
(i) Method of data collection is very costly.
(ii) Untrained and inefficient investigator can collect erroneous information.
(iii) Partiality and prejudices of the investigator deteriorates the quality of data.
(iv) Sometimes, the data are collected based on assumptions which makes the data
undependable.
1.5.2 Methods of Secondary Data Collection
There are no proper methods for the collection of secondary data. Generally,
secondary data are collected from two main sources:
1. Published sources
2. Unpublished sources.
18 1 Concept, Types, Collection, Classification …
1.5.2.1 Published Sources
Numerous secondary data are collected from the published reports, records and docu-
ments of government offices and other non-government departments and agencies.
Government and non-government departments and agencies prepare and publish
different reports, records and documents on various subjects. Data are often collected
by the researcher or investigator from those published sources.
Example The main sources of collecting data under this method are (a) publications
of government, (b) reports of different commissions and committees, (c) reports and
publications of trade associations and chambers of commerce, (d) market reports and
business bulletins of stock exchanges, (e) economic, commercial and technical jour-
nals, (f) publications of researchers and research institutions etc. Secondary data are
published by different organizations like United Nations Organization (UNO), Inter-
national Monitory Fund (IMF), Food and Agricultural Organization (FAO), World
Bank, UNESCO, UNICEF, Indian Statistical Institution (ISI) etc. In India, National
Remote Sensing Agency (NRSA), SIO, National Atlas and ThematicMappingOrga-
nization (NATMO), Geological Survey of India (GSI), IMO, SSI etc. are important
sources of various geographical maps and data.
1.5.2.2 Unpublished Sources
Sometimes, the collected primary data are not properly published by the collector,
called unpublished data. The researcher collects those unpublished data for their
own need from the collector individual or institution through personal connection
and relationship. For example, unpublished thesis paper of a scholar, records and
documents stored in different governmental and non-governmental offices etc. are
unpublished sources of secondary data.
1.5.2.3 Advantages and Disadvantages of Secondary Data Collection
Advantages
(i) It helps in furnishing reliable information and reliable data.
(ii) This method of data collection is inexpensive. The cost of data collection is
borne by governmental and other non-governmental departments, offices and
agencies.
Disadvantages
(i) The unit of the published data may not be same as it was in the collected
primary data. So, the data collected from published sources may not serve the
purposes.
1.5 Methods of Data Collection 19
(ii) The basis of classification and the method of collection of data may also
be different in governmental and non-governmental sources from which the
secondary data are collected. Due to this, the data may not be appropriate for
the fulfilment of the purpose of the researcher.
Detailed and careful scrutiny and verification of the data before putting them into
use is the prerequisite condition of this method. The researcher or user of the data
should scrutinize the data cautiously in order to knowwhether the data are appropriate
for the purpose for which they are intended. Before the collection of those data, the
following points may be taken into consideration: (1) the scope and objectives of the
study for which the data were actually procured (2) units of the collected primary
data (3) methods adopted for the collection of data (4) degree of authenticity and
accuracy of the data (5) honesty and reliability of the authorities who collected the
data.
1.6 Measurement Scales in Geographical System
Measurement can be defined as assigning the names and quantifying the earth surface
features and working out the relationship using them. In general, measurement refers
to the quantitative description (numerical value) of some properties or attributes of
objects or events for comparing one object or event with others. It offers a platform
to describe the attributes and to communicate this description with others. Measure-
ments or data are the rawmaterialsof descriptive and inferential statistics with which
statistical techniques do work. Data includes facts or figures recorded as an outcome
of measuring or counting a system and from which reliable inferences are made.
After the procurement and recording of the data regarding spatial or temporal
distribution of any phenomenon or event or object, it needs to be properly catego-
rized and summarized in numerical forms. This method of categorizing the collected
raw data involves four different processes of measurement providing four types of
‘number scales’. These are:
(a) Nominal scale
(b) Ordinal scale
(c) Interval scale
(d) Ratio scale
1.6.1 Nominal Scale
It is the basic and simple form of measurement in which data are expressed in terms
of identity only like male or female, lowland or highland, unreserved or reserved
category, present or absent etc. So, the nominal scale is similar to the binary scale
in which the presence of any character or phenomenon is expressed by the value ‘1’
20 1 Concept, Types, Collection, Classification …
and the absence by ‘0’ (Pal 1998). Tossing of a coin which gives either head or tail
is the classical example of a nominal scale.
1.6.1.1 Characteristics of Nominal Data
a. Data should be exhaustive (includes all events or phenomena under study) and
mutually exclusive (no value is laid in two or more category).
b. The items in each category are counted and the total is represented by a number.
c. Data can’t be manipulated by any basic mathematical operation (addition,
subtraction, multiplication, division etc.).
d. It is termed as count data in the form of frequencies.
e. All observations or items within each category are treated as same.
1.6.1.2 Application in Geographical Study
It is used for the determination of equality or differences between geographical
phenomena or events. ‘Mode’ is used only as the measurement of central tendency
in nominal data. Frequency, binomial and multinomial expression is easy in this type
of data.
Examples Classification of land use pattern (forest land, cultivated land, built-up
land etc.); soil, rock or mineral classification etc. belong to nominal scale. Table
1.2 shows the number of male and female students in different departments as an
example of nominal scale measurement.
1.6.2 Ordinal Scale
It is the level of measurement superior to nominal scale. In this method, there is
sufficient information to place the data before or after another along a scale in rank
order either individually or in groups. The differences between objects or events by
their identities can easily be established by this method. The statement X < Y < Z
Table 1.2 Nominal data
(Number of male and female
students in different
departments)
Departments Number of students
Male Female
Mathematics 35 15
Statistics 28 22
Physics 32 18
Chemistry 29 21
Geography 27 23
1.6 Measurement Scales in Geographical System 21
indicates that there are three values or classes of any object or phenomenon in which
value or class X is less than value or class Y and again Y is less than value or class
Z.
1.6.2.1 Characteristics of Ordinal Data
a. The direction and relative position of values on this scale are known.
b. The differences between objects or events by their identities can easily be
established.
c. Application of mathematical operation (addition, subtraction, multiplication,
division etc.) is not possible.
d. The actual differences between values can’t be understood.
e. Some data are inherently ordinal in nature.
1.6.2.2 Application in Geographical Study
It is applied for the determination of greater or lesser values of observations related to
any geographical phenomena or events, i.e. rank of different values of any observation
can easily be identified in this scale. Mode, median, percentile and inter-quartile
range (quartile deviation) are widely used as the measurement of central tendency
and dispersion of values.
Examples Classification of families of any region into rich, upper class, upper-
middle class, middle class, lower-middle class and lower class according to their
socio-economic status is an example of ordinal scale. Similarly, the ranking of Indian
states according to the literacy rate of the people is done using this scale (Table 1.3).
Moh’s scale of hardness of minerals is another example of ordinal scale (Table 1.4).
1.6.3 Interval Scale
Interval scale consists of measures for which there are equal intervals between each
measurement or each group. Thus, interval scales are numeric scales in which not
Table 1.3 Ordinal data (Literacy rate of few Indian states, 2011)
Name of states Literacy rate (%) Rank Name of states Literacy rate (%) Rank
Kerala 93.91 1 Maharashtra 82.91 6
Mizoram 91.58 2 Sikkim 82.20 7
Tripura 87.75 3 Tamil Nadu 80.33 8
Goa 87.40 4 Nagaland 80.11 9
Himachal Pradesh 83.78 5 Manipur 79.85 10
22 1 Concept, Types, Collection, Classification …
Table 1.4 Moh’s scale of
hardness of minerals (Ordinal
scale)
Hardness Mineral Hardness Mineral
1 Talc 6 Feldspar
2 Gypsum 7 Quartzite
3 Calcite 8 Topaz
4 Fluorite 9 Corundum
5 Apatite 10 Diamond
only the objects are given identities and ranked like nominal and ordinal scales but
also the exact differences or intervals between objects in terms of their property are
known. This is capable of comparing the differences between a number of pairs or
values to specify the exact location of the objects along a continuous scale.
1.6.3.1 Characteristics of Interval Data
a. Direction and magnitude of position on scale are known.
b. The exact difference between any two values on the scale is known but there is
an arbitrary point and a unit of measurement.
c. The interval scaled data can easily be added or subtracted but multiplication or
division is not possible.
d. It represents precise idea about all the values of the data.
e. In this scale, the value of zero is arbitrary; absolute zero (true zero) is not used.
For example, the zero (0) value in pH scale is arbitrary.
1.6.3.2 Application in Geographical Study
It is used for the determination of equality or differences of intervals of the values
in arithmetical sense. Interval scales are very applicable as the area of statistical
analysis of geographical data sets opens up. Central tendency can be measured by
mean, median or mode; variance, mean deviation and standard deviation can also be
used as the measure of dispersion.
Examples Celsius temperature scale is the standard example of an interval scale
as the difference between each value is same. The difference between 50 and 40
degree Celsius is a measurable 10 degree Celsius, as is the difference between 90
and 80 degree Celsius. Time is another classical example of interval scale in which
the increments are recognized, consistent andmeasurable. For instance, time in years
AD or BC. Longitude, compass directions are also the examples of interval scale.
1.6 Measurement Scales in Geographical System 23
1.6.4 Ratio Scale
All the requirements of the interval scale are met in ratio scale, and in addition, it has
an absolute zero scale (Pal 1998). For instance, rainfall scale (either in centimetres or
in inches) has a true zero base. Thus, if a place ‘A’ receives 60 cm rainfall and place
‘B’ receives 180 cm rainfall in a year, we can conclude that the place ‘B’ receives
three times more rainfall in a year than the place ‘A’. Ratio scale tells us about the
order of values, exact value between units and allows for a wide range of application
of both descriptive and inferential statistics.
1.6.4.1 Characteristics of Ratio Data
a. Two measurements bear the same ratio to each other independent of the units
of measurement.
b. Data are amenable to all types ofmathematical operations (addition, subtraction,
multiplication and division) and to many forms of statistical analysis.
c. Because of its absolute zero, the ratio scale contains maximum amount of
information about any entity.
d. All the ratio variables are also interval variables but all intervalvariables are not
necessarily ratio variables.
1.6.4.2 Application in Geographical Study
Ratio scale offers a wealth of possibilities when statistical data and techniques are
used in geographical analysis. It is applied for the determination of equality or
differences of ratios of the values. Central tendency can be measured by mean,
median or mode; different measures of dispersion, for example, standard deviation
and coefficient of variation can also be easily computed from ratio scales.
Examples Good examples of ratio scales are the measurement of height, weight,
length, streamwater velocity, slope, income of people etc. In all these measurements,
zero point is identical and absolute.
The major characteristics of these four types of scale of measurement are shown
in Table 1.5.
1.7 Processing of Data
Processing of data is very important and the prerequisite condition for the represen-
tation, analysis, explanation and interpretation of the collected data. The main aim
of data processing is to make the data simple and comprehensible to all. Processing
24 1 Concept, Types, Collection, Classification …
Table 1.5 Characteristics of different scales of measurement
Characteristics Nominal scale Ordinal scale Interval scale Ratio scale
The order of values is known No Yes Yes Yes
Counts or frequency distribution Yes Yes Yes Yes
Mean No No Yes Yes
Median No Yes Yes Yes
Mode Yes Yes Yes Yes
Quantification of difference between
each value
No No Yes Yes
Addition or subtraction of values No No Yes Yes
Multiplication or division of values No No No Yes
Absolute or true zero No No No Yes
of data is nothing but the classification, arrangement and summarization of data.
Galtung (1968) mentioned that ‘Processing of data refers to concentrating, recasting
and dealing with data such that they become as amenable to analysis as possible’
(Khan 2006). The main procedure of data processing starts after the editing and
coding of the data. Identification of errors in the collected data and their rectifica-
tions is called data editing. Soon after the collection of data starts, arrangements
should be made to receive and verify the completed forms sequentially. Generally,
many discrepancies, errors and omissions are observed in these completed forms.
The defective forms should immediately be transferred back for necessary correc-
tions. In case of plentiful errors and inconsistencies, the collected data should be
cancelled and new data should be collected again. The completeness, uniformity,
legibility and comprehensibility of the collected data should be checked carefully
during the time of data editing. Data coding is executed after the editing of the data.
Coding of data is the method of assigning numbers or symbols within the data. In
close-ended question, data coding is performed before the collection of the data, but
in open-ended question, data coding is done after the editing of the data.
Threemethods are followed by the geographers and researchers for the processing
of geographical data:
1.7.1 Classification of Data
The method of systematic arrangement of the data into different classes and groups
based on their common characteristics and similarities is known as data classifica-
tion. In the collected data, there is a group which have homogeneous and common
characteristics and other groups of data are dissimilar from each other in terms of
their characteristics. The homogeneous items are categorized into one groupwhile the
dissimilar items into another group. According to Kapur (1995), ‘Classification is the
process by which individuals and items are arranged into groups or classes according
1.7 Processing of Data 25
to their resemblances’. Good and useful classification of data should possess the unit
of being exhaustive,mutually exclusive, stable andflexible.Data classification should
also be specific and must not be ambiguous and clumsy.
1.7.1.1 Objectives of Data Classification
Major objectives of the classification of data are:
(i) To ensure the sequential and systematic arrangement of data based on their
characteristics, resemblances and affinity.
(ii) The nature, characteristics and actual conditions of the data should be under-
stood and explained clearly by highlighting their similarity and dissimilarity
in classification.
(iii) Simplification and summarization of data by reducing their complexities and
ambiguities.
(iv) To make the data suitable for comparison and establishment of their relation-
ship.
(v) To make the data meaningful, comprehensible and easily applicable for
depicting relevant inferences.
1.7.1.2 Characteristics of Ideal Data Classification
Though there is no hard and fast rule for the classification of data, but the following
points should be taken into account during the classification of data:
(a) Homogeneity: Homogeneous and common values should be taken into one
class and uncommon values into other class.
(b) Purpose oriented:Collected data should be classified in tune with the purpose
of the research or investigation.
(c) Clarity: Classification should be clear, simple and easily understandable to
all, complexities should be avoided.
(d) Completeness: All the items or values should be included in the classification
carefully. No item should be eliminated during data classification.
(e) Mutually exclusive: Classes or groups should be mutually exclusive; no item
should be included in more than one class.
(f) Flexibility:Though, stability of the data classification is important, yet the clas-
sification should be made in such a flexible way that further changes become
possible.
1.7.1.3 Types of Classification
Generally, the classification of data is made based on the nature and characteristics
of the collected data and the objectives of the study or investigation. There are four
types of classification of data:
26 1 Concept, Types, Collection, Classification …
Table 1.6 Geographical classification of data (Population densities of some states in India, 2011)
Sl. No Name of states Population density
(persons/sq. Km.)
Sl. No Name of states Population density
(persons/sq. Km.)
1 Bihar 1102 6 Arunachal Pradesh 17
2 West Bengal 1029 7 Mizoram 52
3 Kerala 859 8 Sikkim 86
4 Uttar Pradesh 828 9 Nagaland 119
5 Tamil Nadu 555 10 Manipur 122
Table 1.7 Chronological classification of data (Decadal growth rate of population in India, 1901–
2011)
Sl. No Name of States Decadal growth
rate of population
Sl. No Name of States Decadal growth
rate of population
1 1901 – 7 1961 21.64
2 1911 5.75 8 1971 24.80
3 1921 –0.31 9 1981 24.66
4 1931 11.00 10 1991 23.87
5 1941 14.22 11 2001 21.54
6 1951 13.31 12 2011 17.64
Geographical Classification (Based on Location or Space)
In this type, data regarding phenomena, events or objects are always measured and
classified based on their geographical distribution and location. It is also called
locational or spatial classification. For example, classification of state-wise produc-
tion of rice in India, state-wise population density in India (Table 1.6), district-wise
Scheduled Caste population in West Bengal etc.
Chronological Classification (Based on Time or Period)
In this type of classification, data are measured and arranged in sequence of time
(chronologically) and classified according to the time bywhich the data aremeasured.
The change of phenomena or events with respect to time is represented in this classi-
fication. For example, classification of month-wise water discharge in a river, year-
wise total rainfall in India, decadal growth rate of population in India (Table 1.7),
year-wise production of coal in India etc.
1.7 Processing of Data 27
Fig. 1.1 Qualitative
classification of data
(population)
Table 1.8 Quantitative classification of data (Monthly income of a group of people)
Sl. No Monthly income Number of people Sl. No Monthly income Number of people
1 Rs.5000–10000 25 6 Rs.30000–35000 14
2 Rs.10000–15000 28 7 Rs.35000–40000 21
3 Rs.15000–20000 18 8 Rs.40000–45000 12
4Rs.20000–25000 30 9 Rs.45000–50000 10
5 Rs.25000–30000 45 10 Rs.50000–55000 15
Qualitative Classification (Attribute)
This type of classification is based on descriptive characteristic or quality of data and
is in accordance with non-measurable terms, like occupation, employment, religion,
caste, literacy etc. (Fig. 1.1). If one group possesses a particular attribute, the other
groupwill possess the opposite or other attribute. For example, if one group of people
is literate, the other groupwill be illiterate. Similarly, if one group of people is honest,
the other group will be dishonest.
Quantitative Classification (Numerical)
Quantitative characteristic of data (variable) which can bemeasured and expressed in
numerical forms is the main basis of this type of classification. For example, monthly
income of a group of people can be measured numerically, such as Rs. 12,000, Rs.
16,000, Rs. 20,000, Rs. 30,000 etc. (Table 1.8). Similarly, the monthly expenditure
of people; height, weight and age of people can also be measured in numeric terms.
1.7.2 Tabulation of Data
Tabulation is the orderly and systematic arrangement of numerical data presented in
columns and rows in order to extract information. It summarizes the data in a logical
and orderly manner for the reasons of presentation, comparison and interpretation
andmakes the data brief and concise as they contain only the relevant figures.Gregory
and Ward (1967) mentioned that ‘Tabulation is the process of condensing classified
data in the form of a table, so that it may be more easily understood and so that
any comparisons involved may be more readily made’. The main aim of tabulation
28 1 Concept, Types, Collection, Classification …
of data is to put the whole data set in a concise and logical manner. Connor (1937)
stated that ‘Table involves the orderly and systematic presentation of numerical data
in a form designed to elucidate the problem under consideration’.
1.7.2.1 Essentials of an Ideal Table
No idealmethod is there in the tabulation of data. Skill of data tabulation is generally a
function of years of experience of the researcher. Nevertheless, the researcher should
follow the following rules while tabulating the statistical information (Fig. 1.2):
1. Table number: When many tables are used, then they should be numbered
like Tables 1 and 2 etc. for future reference. In case of several columns (more
than four), they should also be numbered serially (Das 2009).
2. Title of table: Each table must have a clear and concise title which will convey
the contents of the table.
3. Stub: Stub is the left-most column of the table which is clear and self-
explanatory and used for representing the items and their headings. It is
generally marked with rows in which an item is mentioned.
4. Caption: It is the title for columns other than the stub consisting of the upper
part of the table.
Fig. 1.2 Different parts of an ideal table
1.7 Processing of Data 29
5. Body of the table: It is the main part of the table containing the clear and
distinctive figures and data which are displayed in the table.
6. Unit ofmeasurement:Units ofmeasurement likeKg. forweight, ft. for height,
Rs. for price etc. must be clearly mentioned in the column headings.
7. Simplicity: The table must be clear and simple keeping a balance between
length and breadth in which the figures or values should be shown distinctly.
The main columns and sub-columns should be indicated by heavy lines and
light lines, respectively. The important figures in the table should be indicated
by putting them in prominent place or in bold type.
8. Arrangement: The arrangement of data in the table depends on the nature
of data, type of the table and the purposes for which they are intended. Data
should be arranged in a logical sequence in the table. For example, the time
series data must be arranged chronologically.
9. Comparability: The data should be arranged in the table in such a way that
they become easy to compare. Comparable columns of figures should be kept
as close as possible. In case of percentage figures, the basis of calculation of
percentage should be mentioned near the figures to which they relate. Large
number of figures should be rounded and indicated in thousands, millions etc.
10. Source: If the data have been collected and compiled from other sources, the
source must be mentioned clearly in the foot-note.
11. Total: The total numbers of column must be mentioned at the bottom of the
table and the row totals, if useful should also be mentioned.
12. Foot-note: The specific explanation about the figures should be mentioned as
foot-note by using symbol (*), numbers (1, 2, 3,….) or English small letters
(a, b, c,…).
Example A blank table has been prepared (Table 1.9) to show the discharge of water
in pre-monsoon, monsoon and post-monsoon seasons by dividing into respective
months during high and low tide at the places of Kolaghat, Soyadighi, Anantapur,
Pyratungi, Dhanipur and Geonkhali on Rupnarayan River.
1.7.2.2 Types of Table
On the basis of purpose and uses, tables are of two types:
General Purpose Table
General purpose table, also called reference table, is generally voluminous in size
and used as a repository of information. Special care and attention is required for
the preparation of such table and the tabulation of information in it, because the
informationneeded for referencemaybeobtained readilywithout any loss of time and
effort (Bose 1980). These tables are prepared frequently by the concerned authority.
30 1 Concept, Types, Collection, Classification …
Ta
bl
e
1.
9
B
la
nk
ta
bl
e
to
sh
ow
se
as
on
-w
is
e
w
at
er
di
sc
ha
rg
e
in
R
up
na
ra
ya
n
R
iv
er
Se
as
on
M
on
th
W
at
er
di
sc
ha
rg
e
(m
3
/s
ec
)
K
ol
ag
ha
t
So
ya
di
gh
i
A
na
nt
ap
ur
P
yr
at
un
gi
D
ha
ni
pu
r
G
eo
nk
ha
li
H
ig
h
tid
e
L
ow
tid
e
H
ig
h
tid
e
L
ow
tid
e
H
ig
h
tid
e
L
ow
tid
e
H
ig
h
tid
e
L
ow
tid
e
H
ig
h
tid
e
L
ow
tid
e
H
ig
h
tid
e
L
ow
tid
e
Pr
e-
m
on
so
on
Fe
br
ua
ry
M
ar
ch
A
pr
il
M
ay
A
ve
ra
ge
M
on
so
on
Ju
ne
Ju
ly
A
ug
us
t
Se
pt
em
be
r
A
ve
ra
ge
Po
st
-m
on
so
on
O
ct
ob
er
N
ov
em
be
r
D
ec
em
be
r
Ja
nu
ar
y
A
ve
ra
ge
1.7 Processing of Data 31
Table 1.10 Simple table
(Population size of some
selected countries, 2011)
Name of the country Total population (million)
China 1360
India 1210
USA 304
Indonesia 229
Brazil 193
Pakistan 165
Source Human Development Report 2011, Oxford University
Press, New Delhi.
Example The reports in tabular form prepared by different governmental and
government-aided offices are the examples of general purpose table.
Special Purpose Table
Special purpose table or text table or summary table contains the summary of infor-
mation and is used for special purposes. Generally, the table is small in size and
prepared from the information gathered in the reference table. These tables are
prepared suddenly.
Example Table prepared with the data collected about the smokers in India is a
special purpose table.
Again, on the basis of nature and characteristics of classification of data, tables
are of two types:
Simple Table
A simple table contains the data representing one characteristic only; information
relating to other characteristics is left out (Table 1.10).
Complex Table
Complex table contains the data representing several characteristics. It shows the
figures corresponding to a number of items (Table 1.11).
32 1 Concept, Types, Collection, Classification …
Table 1.11 Complex table
(Hypothetical state of the
Earth’s atmosphere)
Altitude (m) Hypothetical state of the Earth’s atmosphere
Pressure
(MPa)
Temperature
(°C)
Density
(kg/m3)
0 0.1013 15.0 1.225
1000 0.898 8.5 1.1117
2000 0.759 2.0 1.0581
3000 0.701 –4.5 0.9093
1.7.3 Frequency Distribution
It is the method by which all the observations of a series are divided into a number
of classes or groups, and the corresponding number of observations under each class
areshown against its respective class. The number of times each value occurs is
called frequency, and the table in which the distribution of observations against each
variable or class of variables is shown is known as frequency distribution table or
frequency table. A frequency distribution table contains a condensed summary of the
original data. It represents not only the range of the values of a data series, but also
shows the nature of their distribution throughout the range of the series.
The summarization of data into frequency distribution table entails much loss of
details of the data. But it is very helpful and is an effective way for the treatment
and interpretation of large volume of data. Some values, like different central values,
values of dispersion and variability etc. of the data may be calculated easily from
the frequency distribution table. The raw data (unorganized data having no form and
structure) have no value in statistical analysis and interpretation. Array (arranged
data in order of magnitude either in descending or in ascending order) has little
significance in statistical analysis and interpretation. Frequency distribution of a
large volume of information is very useful and significant in statistical analysis and
interpretation.
On the basis of their nature, frequency distributions are of two types:
Simple (ungrouped) frequency distribution
In this type, the observations are not divided into groups or classes, the values of
variables are shown individually (Table 1.12).
Grouped frequency distribution
In this type, the observations are divided into different classes or groups and the
number observations in each class are shown as frequency (Table 1.13).
1.7.3.1 Important Terminologies Associated with Grouped Frequency
Distribution
In grouped frequency distribution, the following terms are very useful and significant:
(a) Class or class interval
1.7 Processing of Data 33
Table 1.12 Simple
frequency distribution
Amount of rainfall (mm) Frequency (Number of rainy days)
60 12
61 10
62 8
63 15
64 11
65 7
66 5
Table 1.13 Grouped
frequency distribution
Class interval (Temperature in
°C)
Frequency (Number of days)
11–15 37
16–20 31
21–25 43
26–30 19
31–35 9
36–40 6
41–45 5
(b) Class limit (lower class limit and upper class limit)
(c) Class boundary (lower class boundary and upper class boundary)
(d) Class frequency ( f i ) and Total frequency (N)
(e) Class mark or mid-value or mid-point of class interval (xi )
(f) Class width or size of class interval (wi )
(g) Frequency density ( f di )
(h) Relative frequency (R f i )
(i) Percentage frequency
(a) Class or class interval: Large number of observations having wide range is
usually classified into several groups according to the size of values. These
groups are called class interval or simply classes. In Table 1.14, column (1),
the class interval of temperatures (in °C) are 11–15, 16–20 etc. There are seven
classes in the frequency distribution, the last class being 41–45.
Two ends of the classes are defined by class limits or boundaries. When two ends
of a class are clearly specified, then it is called closed-end class but the class, in
which one end is not clearly specified, is called an open-end class. When relatively
few observations are far apart from the rest, then the construction of open-ended
classes is required. Classes having no or zero frequency are called empty classes.
(b) Class limit (Lower class limit and Upper class limit): In case of grouped
frequency distribution, the classes or class intervals, specified by pairs of values
are arranged in such a way that the upper end (upper value) of one class does
34 1 Concept, Types, Collection, Classification …
Ta
bl
e
1.
14
Fr
eq
ue
nc
y
di
st
ri
bu
tio
n
ta
bl
e
(B
as
ed
on
th
e
da
ta
fr
om
Ta
bl
e
1.
13
)
C
la
ss
In
te
rv
al
[1
]
C
la
ss
Fr
eq
ue
nc
y
(f
i)
[2
]
C
la
ss
L
im
it
C
la
ss
B
ou
nd
ar
y
C
la
ss
M
ar
k
(x
i)
[7
]
W
id
th
of
C
la
ss
(w
i)
[8
]
Fr
eq
ue
nc
y
D
en
si
ty
(f
d
i)
[9
]
R
el
at
iv
e
fr
eq
ue
nc
y
(R
f i
)
[1
0]
Pe
rc
en
ta
ge
fr
eq
ue
nc
y
[1
1]
L
ow
er
[3
]
U
pp
er
[4
]
L
ow
er
[5
]
U
pp
er
[6
]
11
–1
5
37
11
15
10
.5
15
.5
13
5
7.
4
0.
24
7
24
.7
16
–2
0
31
16
20
15
.5
20
.5
18
5
6.
2
0.
20
7
20
.7
21
–2
5
43
21
25
20
.5
25
.5
23
5
8.
6
0.
28
6
28
.6
26
–3
0
19
26
30
25
.5
30
.5
28
5
3.
8
0.
12
7
12
.7
31
–3
5
9
31
35
30
.5
35
.5
33
5
1.
8
0.
06
6
36
–4
0
6
36
40
35
.5
40
.5
38
5
1.
2
0.
04
4
41
–4
5
5
41
45
40
.5
45
.5
43
5
1
0.
03
3
3.
3
To
ta
l
N
=
∑
f i
15
0
1.
00
10
0
1.7 Processing of Data 35
not coincide with the lower end (lower value) of the immediately following
class. These two extreme values, used to specify the limits of a class for the
purpose of tallying the original observations into different classes are known as
‘Class Limits’. The smaller value (lower end value) of the pair is called lower
class limit, whereas the larger value (upper end value) is called upper class
limit of a particular class (Sarkar 2015). In Table 1.14, the values 11, 16, 21,
26, 31, 36 and 41 (in column 3) are lower class limits, while the values 15, 20,
25, 30, 35, 40 and 45 (in column 4) are the upper class limits.
(c) Class boundary (Lower class boundary and Upper class boundary): Class
boundaries are the limits up to which the two limits of each class may be
extended to fill up the gapwhich exists between classes (Bose 1980). The upper
boundary of one class coincides with the lower boundary of the immediately
following class. The lower extreme value of the two boundaries is called the
lower class boundary and the upper extreme value of the same is called the
upper class boundary (columns 5 and 6 in Table 1.14).
Class boundary is calculated from class limit using the following formula:
Lower Class Boundary =
[
Lower Class Limit −
(
d
2
)]
(1.1)
Upper Class Boundary =
[
Upper Class Limit +
(
d
2
)]
(1.2)
where ‘d’ is the common difference between the upper class limit of any class
(class interval) and the lower class limit of the next class (class interval). The obser-
vations are recorded to the nearest unit, d = 1 or the nearest tenth of a unit, d = 0.1
etc.
(d) Class frequency and Total frequency: Class frequency or simply Frequency
is the number of observations (values) lying within a class. It is denoted by f i .
Total frequency (N) is the sum of all the class frequencies in a distribution.
In other words, if all the class frequencies in a distribution are summed up,
it indicates the total frequency. Total frequency shows the total number of
observations considered in the frequency distribution. In Table 1.14, the class
frequencies are 37, 31, 43,…5 (column 2) and the total frequency is 150. The
working formula of total frequency (N) is as follows:
N =
n∑
i=1
fi (1.3)
where n = number of class
f i= frequency of the ith class.
(e) Class mark or mid-value or mid-point of class interval: The value lying
exactly at the middle of a class interval is called class mark or mid-value (13,
18, 23…43 are the class mark in column 7 in Table 1.14). The working formula
36 1 Concept, Types, Collection, Classification …
for class mark is as follows:
Class Mark (xi ) = Lower Class Limit +Upper Class Limit
2
(1.4)
Or,Class Mark (xi ) = Lower Class Boundary +Upper Class Boundary
2
(1.5)
The mid-value of the class or the class mark is considered as the representa-
tive value of the class for the computation of descriptive statistics like mean, mean
deviation, standard deviation etc.
(f) Class width or size of class interval: The difference between the lower and
upper class boundaries (but not class limits) is called class width or size of
class interval. In Table 1.14, 5 is the class width (column 8) of this frequency
distribution.
Width of class(wi ) = [Upper class boundary − Lower class boundary]
(1.6)
Generally, in a frequency distribution, equal width of the classes is preferred as it
simplifies thecalculation of some statistical measures (mean, median, mode, mean
deviation, standard deviation etc.) in short-cut method. But in few cases, classes of
unequal size may also be constructed when the values are highly dispersed in nature
and some of them are few and far away from the rest. In such cases, the use of equal
width may result in some ‘Empty classes’, i.e. classes with zero frequency.
(g) Frequency density: Number of frequency per unit class width is called the
frequency density of a class. More the number of frequency per unit class
width, more the frequency density and vice versa. The degree of concentration
of frequency in a particular class is represented by the frequency density and
is calculated by the following formula:
Frequency densi ty( fdi ) = Class Frequency
Class width
= fi
wi
(1.7)
In Table 1.14, the frequency densities of different classes are 7.4, 6.2, 8.6 etc.
(Column 9). Frequency density is used for the drawing of histogram in case of
frequency distribution having unequal class width.
(h) Relative frequency: In a frequency distribution, the ratio between frequency
of a particular class ( fi ) and the total frequency (N ) of the distribution is called
relative frequency (R f i ). The sum of all relative frequency in a distribution is
equal to unity (1).
Relative Frequency (R fi ) =
(
fi
N
)
(1.8)
1.7 Processing of Data 37
and
n∑
i=1
R fi = 1 (1.9)
where n = number of classes.
In Table 1.14, the relative frequencies of different classes are 0.247, 0.207, 0.286
etc. (Column 10).
(i) Percentage frequency: Percentage frequency is the class frequency when
expressed as a percentage of the total frequency. In other words, when relative
frequency is expressed in terms of percentage, then it is called as percentage
frequency.
Percentage f requency = Class f requency
T otal f requency
× 100 (1.10)
In Table 1.14, the percentage frequencies of different classes are 24.7, 20.7, 28.6
etc. (Column 11). The sum of all percentage frequencies in a distribution is equal to
hundred percentage (100%).
1.7.3.2 Construction of Frequency Distribution Table
In grouped frequency distribution, themain questions are: (a) selection of the number
of classes, (b) selection of class width and (c) selection of class limits and boundaries.
(a) Selection of the number of classes: There is no hard and fast rule in selecting
the number of classes into which the observations would be divided. Generally,
it depends on the nature of the data, number of observations in the series and
the purpose for which the data are intended. It is generally agreed that the
number of classes should neither be very large (to avoid lengthy and unwieldy
frequency distribution) nor very small (information will be lost and the true
pattern of the distribution of observations will be obscured). Normally, the
number of classes should lie between 5 and 15, depending on the number of
observations available. In case of small number of observations, some authors
suggest the use of Sturges’ formula:
n = 1 + 3.3 logN (1.11)
where, n is the number of classes and N is the total number of observations in the
data series.
(b) Selection of class width: Selection of the class width depends on the number
of observations in the data series and the number of classes into which the
observations are divided. For this purpose, at first we have to calculate the
38 1 Concept, Types, Collection, Classification …
range (difference between highest and lowest value of the observations) of the
data. If we like to have classes of equal width, then the width of the classes can
be obtained by the formula:
Class width = Range(Highest value of the series − Lowest value of the series)
Number of classes
(1.12)
Or, Class width = Range(Highest value of the series − Lowest value of the series)
1 + 3.3 log N
(1.13)
Similarly, if the class width is known, the number of classes of the frequency
distribution can be calculated by:
Number of classes = Range(Highest value of the series − Lowest value of the series)
Class width
(1.14)
Example If the maximum and minimum values in a data series are 865 and 105,
respectively, then the range of data will be 887–105 = 782. In case of 8 number of
classes, the width of classes (wi ) will be 782
8 = 97.75. It is very important to note
that if the range of the data set is approximated to its nearest round figure which can
easily be divided by the number of classes (n), the width of the class becomes easily
recognizable andmore comprehensive. In case of the above example,maximumvalue
of 887 can be considered as 900 and the minimum value of 105 can be considered
as 100. Thus, the range of the data becomes 900–100 = 800 and the class width for
8 numbers of classes will be 900−100
8 = 800
8 = 100. So, the class width of 97.75 can
easily be modified to 100 for practical applications.
Consideration of class width is very significant because it is an important deter-
minant for the selection of class limits, class boundaries and class mark which are
essentially used not only in preparing the frequency distribution table but also in the
computations of different descriptive statistical measures (Sarkar 2015).
(c) Selection of class limits and boundaries: Selection of class limit is made in
two ways.
(i) Exclusive method
(ii) Inclusive method
(i) Exclusive method: In this method, the upper limit of one class coincides with
the lower limit of the next class, i.e. the upper limit of one class and the lower limit
of the following class have the same figure and the same value. For example, 25–35,
35–45, 45–55 etc. (Table 1.15).
In this situation, the problem arises on account that in which class a value identical
to the coinciding limits would be included. The problem is solved by excluding the
identical value from the previous class and including it in the following class. In this
sense, the upper limit of each class is considered as less than that limit while the
lower limit of each class represents the exact value. Then, the class intervals of the
above example will be stated as 25 to less than 35, 35 to less than 45, 45 to less than
55 etc.
1.7 Processing of Data 39
Table 1.15 Exclusive and
inclusive methods of selection
of class limit
Exclusive method Inclusive method
Class limit
(Weight in kg)
Frequency
(Number of
persons)
Class limit
(Number of
workers)
Frequency
(Number of
factory)
25–35 6 25–34 5
35–45 4 35–44 5
45–55 8 45–54 7
55–65 3 55–64 3
65–75 4 65–74 5
(ii) Inclusive method: In this method, the lower limit and upper limit of a partic-
ular class are included within the same class. Thus, the upper limit of one class does
not coincide with the lower limit of the following class. Due to this, a gap exists
between the upper limit of one class and the lower limit of the following class. For
example, 25–34, 35–44, 45–54 etc. (Table 1.15). Thismethod of classificationmay be
applied for the grouped frequency distribution of discrete variables, such as number
of family members, number of households, number of industrial workers etc., which
can occur in integral values only. This method is not suitable to use in variables with
fractional values like temperature, weight, height etc.
Thus, the nature and characteristics of the variable (continuous or discrete) under
observation is important to decide whether the exclusive method or the inclusive
method should be used for the selection of class limits. Exclusive method must be
used for the classification of continuous variables whereas the inclusive method is
suitable in case of discrete variables.
A frequency distribution table is drawn with (n + 1) rows and 6 columns (for
equal class width) or 7 columns (for unequal class width). The column heads, from
left to right are: class limits, class boundaries, class mark (xi ), class width (wi ), tally
marks and frequency ( f i ). In case of unequal classes, an additional column with
headings of frequency density ( fi
wi
) is drawn.
Example-1 Heights (in metre) of 35 places frommean sea level are given below.
Prepare a frequency distribution table from the given data.
412 350 307 308 432 342 357 297 328 375 356 429 329 240.
353 403 355 404 350 335 304 332 281 335 361 266 324 302.
406 366 337 345 343 227 364.
Solution:
Number of classes (n) = 1 + 3.3 log N.
= 1 + 3.3 log 35 [N = number of observations].
= 6.1294.
= 6 (nearest round figure).
Class width (w) = Range (Highest value of the series−Lowest value of the series)
Number of classes
= 432m−227m
6= 34.17 m.
= 35 m.
40 1 Concept, Types, Collection, Classification …
Table 1.16 Frequency distribution table showing the height (in metre) from mean sea level
Class limit
(Height in m)
Class
Boundary
(Height in m)
Class mark
(xi )
Class width
(wi )
Tally marks Frequency ( fi )
227–261 226.5–261.5 244 35 2
262–296 261.5–296.5 279 35 2
297–331 296.5–331.5 314 35 8
332–366 331.5–366.5 349 35 16
367–401 366.5–401.5 384 35 1
402–436 401.5–436.5 419 35 6
Total N = ∑
f i =
35
Example-2 Meanmonthly temperature (in °F) of 40 places are given below. Prepare
a frequency distribution table from the given data.
29.4 49.5 39.6 45.7 53.8 39.7 36.6 58.7 34.4 39.7
54.4 54.7 51.5 62.5 23.0 80.8 30.3 27.7 44.0 35.7
56.1 60.2 72.2 50.8 33.4 56.3 32.4 59.2 48.2 45.1
42.7 52.1 24.2 68.6 66.0 39.5 43.4 36.4 44.1 56.6
Solution:
Number of classes (n) = 1 + 3.3 log N.
= 1 + 3.3 log 40 [N = number of observations].
= 6.32.
= 6 (nearest round figure).
Class width(w) = Range (Highest value of the series − Lowest value of the series)
Number of classes
= 80.8 0F − 23.0 0F
6
= 9.63 0F
= 10 0F
1.7 Processing of Data 41
Table 1.17 Frequency distribution table showing the mean monthly temperature (°F)
Class limit
(Temperature
in °F)
Class
Boundary
(Temperature
in °F)
Class mark
(xi )
Class width
(wi )
Tally marks Frequency ( fi )
23.0–32.9 22.95–32.95 27.95 10 6
33.0–42.9 32.95–42.95 37.95 10 10
43.0–52.9 42.95–52.95 47.95 10 10
53.0–62.9 52.95–62.95 57.95 10 10
63.0–72.9 62.95–72.95 67.95 10 3
73.0–82.9 72.95–82.95 77.95 10 1
Total N = ∑
fi =
40
1.7.3.3 Cumulative Frequency Distribution
The accumulated frequency upto or above some value of the variable is known as
‘Cumulative frequency’. Cumulative frequency corresponding to a particular value of
the variable can be defined as the number of observations smaller than or greater than
that value (Das 2009). A cumulative frequency distribution is a form of frequency
distribution in which the cumulative frequency upto each class is shown against the
same class (Bose 1980). Cumulative frequency of any class is calculated by adding
the frequency of each class to the total frequency of the previous classes. It represents
the progressive total of the frequencies falling under each class.
A cumulative frequency distribution can be formed in two ways: (i) by less than
method and (ii) by more than method. The number of observations ‘upto’ a given
value is called less than cumulative frequency and the number of observations ‘greater
than’ a value is called more than cumulative frequency. In the less than method, the
frequencies are accumulated from the lowest class to upwards, but in more than
method, the frequencies are accumulated from the highest class to downwards.
1.7.3.4 Uses of Cumulative Frequency Distribution
Cumulative frequency distribution is very significant and useful to determine the
number of observations less than or greater than a particular value. It is very helpful
in finding (a) the number of observations less than or below any given value (b)
the number of observations more than or above any given value (c) the number of
observations falling between two specific values.
42 1 Concept, Types, Collection, Classification …
Table 1.18 Cumulative frequency distribution table using the data of Table 1.16
Class limit
(Height in
m)
Class
Boundary
(Height in
m)
Frequency
( f i )
Cumulative Frequency (F)
Less than F More than F
227–261 226.5–261.5 2 226.5 0 226.5 35 (0 + 6 +
1 + 16 + 8
+ 2 + 2)
262–296 261.5–296.5 2 261.5 2 (0 + 2) 261.5 33 (0 + 6 +
1 + 16 + 8
+ 2)
297–331 296.5–331.5 8 296.5 4 (0 + 2 +
2)
296.5 31 (0 + 6 +
1 + 16 + 8)
332–366 331.5–366.5 16 331.5 12 (0 + 2 +
2 + 8)
331.5 23 (0 + 6 +
1 + 16)
367–401 366.5–401.5 1 366.5 28 (0 + 2 +
2 + 8 + 16)
366.5 7 (0 + 6 +
1)
402–436 401.5–436.5 6 401.5 29 (0 + 2 +
2 + 8 + 16
+ 1)
401.5 6 (0 + 6)
N = ∑
f i
= 35
436.5 35 (0 + 2 +
2 + 8 + 16
+ 1 + 6)
436.5 0
Cumulative frequency may be represented in relative or percentage form.When it
is represented in percentage, it is known as cumulative percentage. It is very helpful
for the comparison between frequencies.
Example-1
See Table 1.18.
Example-2
See Table 1.19.
1.8 Methods of Presentation of Geographical Data
Presentation of data means the demonstration of the data in an attractive and lucid
manner tomake them easily understandable to all. Suitable and accurate visualization
of the collected data becomes helpful for their proper understanding, analysis and
explanation. Geographical data can be represented and portrayed in the following
four ways:
1.8 Methods of Presentation of Geographical Data 43
Table 1.19 Cumulative frequency distribution table using the data of Table 1.17
Class limit
(Temperature
in °F)
Class
Boundary
(Temperature
in °F)
Frequency
( fi )
Cumulative Frequency (F)
Less than F More than F
23.0–32.9 22.95–32.95 6 22.95 0 22.95 40 (0 + 1
+ 3 + 10
+ 10 +
10 + 6)
33.0–42.9 32.95–42.95 10 32.95 6 (0 + 6) 32.95 34 (0 + 1
+ 3 + 10
+ 10 +
10)
43.0–52.9 42.95–52.95 10 42.95 16 (0 + 6
+ 10)
42.95 24 (0 + 1
+ 3 + 10
+ 10)
53.0–62.9 52.95–62.95 10 52.95 26 (0 + 6
+ 10 +
10)
52.95 14 (0 + 1
+ 3 + 10)
63.0–72.9 62.95–72.95 3 62.95 36 (0 + 6
+ 10 +
10 + 10)
62.95 4 (0 + 1
+ 3)
73.0–82.9 72.95–82.95 1 72.95 39 (0 + 6
+ 10 + 10
+ 10 + 3)
72.95 1 (0 + 1)
N = ∑
fi =
40
82.95 40 (0 + 6
+ 10 +
10 + 10
+ 3 + 1)
82.95 0
1.8.1 Textual Form
Textual presentation is themost raw and vague formof representation of geographical
data. In textual form, data are presented in paragraph or in sentences. When the
amount of data is not too large, then this form of presentation is more appropriate and
effective. In textual presentation,mainly the important characteristics are enumerated
giving emphasis on the most significant figures and highlighting the most striking
attributes of the data set. Significant figures and attributes may be the summary
statistics likemaximumandminimumvalue,mean,median,meandeviation, standard
deviation etc.
Example Out of 180 sediment samples studied in Rupnarayan River, approximately,
63.80% of the sediments are very fine sand, 14.76% are fine sand and 21.44% are
coarse silt type. In dry season, more than 60% sediments are moderately to well
sorted but in monsoon season 63.85% sediments are poorly to very poorly sorted.
44 1 Concept, Types, Collection, Classification …
Around 55% of the sediments are of fine and very fine skewed type, 33% of samples
are near symmetrical and remaining 12% are of coarse skewed type.
1.8.1.1 Advantages and Disadvantages of Textual Form
Advantages
1. Easy to understand.
2. It enables one to give emphasis on certain important features of the data
presented.
Disadvantages
1. One has to go through the complete reading of the text for comprehension.
2. Boring to read especially if too lengthy.
3. Reader may skip the statements.
1.8.2 Tabular Form
Tabular presentation of geographical data is very important and easily understand-
able to all. It is one of the most commonly used forms of representation of data
as tables are very easy to construct and understand. A table makes possible repre-
sentation of even large amounts of data in a lucid, attractive and organized manner.
Tabulation is the orderly and systematic arrangement of numerical data presented in
columns and rows in order to extract information. It summarizes the data in a logical
and orderly manner for the reasons of presentation, comparison and interpretation
and makes the data brief and concise as theycontain only the relevant figures (Table
1.20) [Detailed discussion in Sect. 1.7.2].
Table 1.20 Tabular presentation of data (% of sand, silt and clay in bed sediments of Rupnarayan
River)
Locations Sand-silt-mud proportion (%)
Pre-monsoon season Monsoon season Post-monsoon season
Sand Silt Clay Sand Silt Clay Sand Silt Clay
Kolaghat 68–91 8–30 1–15 76–91 8–17 1–12 71–86 9–20 5–20
Soyadighi 60–78 12–25 8–18 70–86 8–21 2–18 70–84 7–21 8–18
Anantapur 45–78 13–48 6–38 59–86 10–42 4–17 55–78 14–39 4–22
Pyratungi 54–79 8–32 12–26 73–87 9–20 4–15 56–85 4–17 9–18
Dhanipur 38–76 11–61 1–41 52–84 10–45 3–18 45–75 24–54 1–25
Geonkhali 46–78 9–40 12–38 61–87 9–18 4–19 49–74 10–32 16–21
Source Field survey and laboratory experiment.
1.8 Methods of Presentation of Geographical Data 45
1.8.2.1 Advantages and Disadvantages of Data Representation in Table
Advantages
The advantages of tabulation of data are as follows:
1. By tabulation, data are arranged systematically and logically in concise form.
2. Tabulation enables the data to be easily understandable and it is more impressive
than textual presentation.
3. It is very useful to detect the errors and exclusions in the data.
4. Recurrence of explanatory terms and phrases can be avoided.
5. The nature and characteristics of data can easily be understood at a glance in
tabular form.
6. Comparison and interpretation of statistical data becomes easy.
Disadvantages
1. Tabular presentation does not give a detailed view of the data, unlike textual
(descriptive) presentation.
2. It is only helpful to identify the differences of points or if we want to tally two
or more things.
1.8.3 Semi-Tabular Form
It is the combination of textual and tabular form of data presentation. This is also
called partial-tabular presentation of data. It is helpful for the easy comparison
because the numerical figures are separately presented from the text.
Example Overall literacy rates in different census years after independence in India
are:
• 16.67% in 1951
• 24.02% in 1961
• 29.45% in 1971
• 36.23% in 1981
• 42.84% in 1991
• 54.51% in 2001
• 64.32% in 2011.
1.8.4 Graphical Form (Graphs, Diagrams and Maps)
In addition to all the above mentioned methods, classified and tabulated geograph-
ical data can suitably and easily be represented through different graphs (line
graph, climograph, Lorenz curve, rank-size graph, frequency graph etc.), diagrams
(bar diagram, pie-diagram, rectangular diagram etc.) and maps (choropleth map,
46 1 Concept, Types, Collection, Classification …
chorochromatic map, choroschematic map etc.). All the graphs, diagrams and maps
are drawn following various geometric methods, thus it is known as geometric repre-
sentation of data. Representation of geographical data by graphical, diagrammatic
and mapping techniques is very popular, attractive and easy to understand to the
geographers, researchers and to the common literate people also.
References
Bose A (1980) Statistics. Calcutta Book House, 1/1 Bankim Chatterjee Street, Calcutta 700073
Connor LR (1937) Statistics in theory & practice, 2nd edn, Sir Isaac Pitman & Sons, Inc
Das NG (2009) Statistical methods, vol. I & II. McGraw Hill Education (India) Pvt Ltd, ISBN:
978-0-07-008327-1
Galtung J (1968) A structural theory of integration. J Peace Res 5(4):375–395
Gregory H, Ward D (1967) Statistics for business studies. McGraw-Hill. ISBN:9780070944909
Kapur SK (1995) Elements of practical statistics. Oxford & IBH Publishing Co Pvt Ltd., NewDelhi
Khan MAT (2006) Quantitative techniques in geography. Perfect Publications, Dhaka. ISBN: 984-
8642-02-1
Pal SK (1998) Statistics for Geoscientists: Techniques and Applications. Concept Publishing
Company, New Delhi. ISBN: 81-7022-712-1
Sarkar A (2015) Practical geography: a systematic approach. Orient Blackswan Private Limited,
Hyderabad, Telengana, India. ISBN: 978-81-250-5903-5
Young PV (1994) Scientific social surveys and research. Prentice Hall of India Private Limited,
New Delhi
Chapter 2
Representation of Geographical Data
Using Graphs
Abstract Suitable, accurate and lucid presentation and visualization of geographical
data using various types of graphs become helpful for their correct analysis, expla-
nation and realization for proper understanding of the real world. It is very simple,
attractive and easily recognizable not only to the geographers or efficient academi-
cians but also to the common literate people. This chapter includes a detailed classifi-
cation of all types of graphs and the discussion of various types of co-ordinate systems
with illustrations as an essential basis of the construction of graphs. Different types of
bi-axial (arithmetic and logarithmic graph, climograph etc.), tri-axial (ternary graph),
multi-axial (spider graph, polar graph etc.) and special graphs (water budget graph,
hydrograph, rating curve,Lorenz curve, rank-size graph, hypsometric curve etc.) have
been discussed with suitable examples in terms of their suitable data structure, neces-
sary numerical calculations, methods of construction, appropriate illustrations, and
advantages and disadvantages of their use. Systematic and step-by-step discussion
of methods of their construction helps the readers for easy and quick understanding
of the graphs. The difference between arithmetic and logarithmic graphs is explained
precisely with proper examples and illustrations. Different types of frequency distri-
bution graphs have been explained with suitable data, necessary mathematical and
statistical computations, and proper illustrations. All types of graphs represent a
perfect co-relation between the theoretical knowledge of various geographical events
and phenomena and their realistic implications with suitable examples.
Keywords Graphs · Co-ordinate system · Bi-axial graph · Arithmetic and
logarithmic graph · Tri-axial graph ·Multi-axial graph · Special graph · Frequency
distribution graph
2.1 Concept of Graph
The method of representation of geographical data in graphs has been developed to
avoid the difficulties arising from their tabular presentation and for their better under-
standing also. This technique is very helpful to understand and explain the relation-
ship between various geographic data, to indicate the trends of different geographic
variables and to make a comparison between them. Graph is the most familiar and
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. K. Maity, Essential Graphical Techniques in Geography, Advances in Geographical
and Environmental Sciences, https://doi.org/10.1007/978-981-16-6585-1_2
47
http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-16-6585-1_2&domain=pdf
https://doi.org/10.1007/978-981-16-6585-1_2
48 2 Representation of Geographical Data Using Graphs
conventional method inwhich a series of geographical data are represented following
a suitable co-ordinate system on a reference frame.
2.2 Types of Co-ordinate System
The four main types of co-ordinate systems are:
(1) Cartesian or rectangular co-ordinate system
(2) Polar co-ordinate system
(3) Cylindrical co-ordinate system
(4) Spherical co-ordinate system
2.2.1 Cartesian or Rectangular Co-ordinate System
Cartesian co-ordinate or rectangular co-ordinate system is a co-ordinate system that
identifies each point distinctively on a plane with the help of a set of numerical co-
ordinates. Co-ordinates are the signed (either positive or negative) distances to the
specific point from two perpendicular oriented lines. Both the co-ordinates and lines
are measured and represented in the same unit of length. This co-ordinate system
provides a technique of portraying graphs and representing the positions of points
on a two-dimensional (2D) surface as well as in a three-dimensional (3D) space.
On a two-dimensional (2D) surface,while constructing a graph, at first a horizontal
line X X ′ called abscissa and a vertical line Y Y ′ called ordinate (both are known as
co-ordinate axes) are drawn which intersecteach other at right angles and the whole
plotting area is divided into four parts called quadrants (Fig. 2.1). The point of
intersection of these two axes is called point of origin (‘O’) or zero-point having
x–y co-ordinate (0, 0). All the distances along these two axes are always measured
from this zero point. The rightward and upward measurement of distances from
the zero point indicates the positive values, whereas the leftward and downward
measurements represent the negative values.Thevalues of both ‘x’ and ‘y’ are positive
in the first quadrant, but in the second quadrant, the values of ‘x’ and ‘y’ are negative
and positive, respectively. In the third quadrant, both ‘x’ and ‘y’ are negative, while
in the fourth quadrant, ‘x’ value is positive but ‘y’ value is negative (Fig. 2.1). Most
of the geographical data collected from field investigations are positive in nature and
hence these data are represented in the first quadrant in which the values of ‘x’ and
‘y’ both are positive. The use of second, third and fourth quadrants are comparatively
less in statistical and geographical analysis.
In Cartesian three-dimensional (3D) space, another important axis oriented at
right angles to the xy plane is added. This axis passes through the origin of
2.2 Types of Co-ordinate System 49
Fig. 2.1 Position of independent and dependent variables in different quadrants (Cartesian co-
ordinate system)
the xy plane and is called the ‘Z’ axis, representing the height. Positions or co-
ordinates of points (‘P’, ‘Q’, ‘R’, ‘S’ in Fig. 2.2) are determined based on the east–
west (x), north–south (y) and up–down (z) displacements of points from the origin
‘O’ (0, 0, 0).
2.2.2 Polar Co-ordinate System
Polar co-ordinate system is another common and important co-ordinate system for
the plane. This two-dimensional co-ordinate system specifies the location of each
point on a plane by the measurement of the distance from a reference point (called
pole) and an angle from a reference direction (called polar axis). The location of the
point is obtained by measuring the signed distance from the origin (pole) and the
given angle (measured counter-clockwise) from the polar axis. For a given distance
from the origin ‘r’ and angle from polar axis ‘θ ’, the co-ordinate of any point (‘P’
in Fig. 2.3) is (r, θ). The pole is characterized by (0, θ) for any value of θ .
Polar co-ordinate system is extended to three dimensions in two methods like
cylindrical co-ordinate system and spherical co-ordinate system.
50 2 Representation of Geographical Data Using Graphs
Fig. 2.2 Determination of location of a point on Cartesian co-ordinate system (3D)
Fig. 2.3 Determination of
location of a point on polar
co-ordinate system
The relation between Cartesian co-ordinate (x, y) and polar co-ordinate (r, θ ) is
that (Fig. 2.3)
sin θ = y
r
(sine function for y) (2.1)
2.2 Types of Co-ordinate System 51
where y = r sin θ
and cos θ = x
r
(cosine function for x) (2.2)
where x = r cos θ .
Again,
r =
√
x2 + y2(Pythagoras theorem to find the long side, i · e. the hypotenuse)
(2.3)
and
θ = tan−1 y
x
(tangent function to find angle) (2.4)
Conversion from Cartesian to polar co-ordinate system
Example: What is (4, 3) in polar co-ordinates?
Solution
Using Pythagoras theorem (Eq. 2.3) we have
r =
√
x2 + y2
r =
√
42 + 32
r = √
16 + 9
r = √
25
r = 5
Using tangent function (Eq. 2.4) we have
θ = tan−1 y
x
θ = tan−1 3
4
θ = tan−10.75
θ = 36.87◦
Answer: The point (4, 3) is (5, 36.87◦) in polar co-ordinates.
52 2 Representation of Geographical Data Using Graphs
Conversion from polar to Cartesian co-ordinate system
Example: What is (5, 36.87◦) in Cartesian co-ordinates?
Solution
Using the sine function (Eq. 2.1) we have
sin θ = y
r
sin θ = y
5
y = 5 × sin 36.87◦
y = 5 × 0.6
y = 3
Using the cosine function (Eq. 2.2) we have
cos θ = x
r
cos θ = x
5
x = 5 × cos 36.87◦
x = 5 × 0.8
x = 4
Answer: The point (5, 36.87◦) is (4, 3) in Cartesian co-ordinates.
2.2.3 Cylindrical Co-ordinate System
Cylindrical co-ordinate system is the extension of the polar co-ordinates by adding
the z-axis along with the height of a right circular cylinder. The z-axis in this co-
ordinate system is the same as in Cartesian co-ordinate system (3D). The addition
of z-axis in polar co-ordinate system gives a triple (r, θ, z) (Fig. 2.4). In some texts,
ρ is used in place of r to denote the distance from the origin to the foot of the
perpendicular to avoid confusion. In terms of Cartesian co-ordinate system
2.2 Types of Co-ordinate System 53
Fig. 2.4 Determination of
location of a point on
cylindrical co-ordinate
system
x = ρ cosθ (2.5)
y = ρ sinθ (2.6)
z = z (height)
Again, in inverse relation these become
ρ =
√
x2 + y2 (2.7)
θ = tan−1 y
x
(2.8)
z = z (height)
54 2 Representation of Geographical Data Using Graphs
2.2.4 Spherical Co-ordinate System
Spherical coordinate (also known as spherical polar coordinate) system is a curvi-
linear coordinate system in which positions of points are defined on a sphere or
spheroid. In spherical co-ordinate, the value of z co-ordinate is converted into φ
giving a triple (r, θ, φ). Here, r is the distance of a point (say P in Fig. 2.5a, b)
from the origin (radial distance) and θ (azimuthal angle) is the angle between the
x-axis and the line joining the origin to P ′, the foot of the perpendicular from the
point P (Fig. 2.5a, b) in the x–y plane. The angle θ is complementary to the longi-
tude [0 ≤ θ < 2π ] and is denoted as λ when referred to as longitude. The angle
φ (polar angle, zenith angle or colatitude) is the angle made by the radius vector
(the vector which connects the point P with origin) with respect to the z-axis. It is
complementary to the latitude [0 ≤ φ ≤ π ] and is represented as φ = 90◦ − δ,
where δ is the latitude. Conventionally, (r, θ, φ) is used in mathematics to represent
radial distance, azimuthal angle and polar angle, respectively. Sometimes, especially
in physics θ and φ are reversely used, i.e. θ indicates polar or zenith angle and φ
indicates azimuthal angle. Then, (r, θ, φ) represent radial distance, polar angle and
azimuthal angle, respectively. In spherical co-ordinate, the symbol ρ is frequently
used instead of r to avoid the confusion with the value r in 2D polar coordinate
systems, i.e. then (r, θ, φ) becomes (ρ, θ, φ).
The transformation from spherical co-ordinates (r, θ, φ) [radial, azimuthal, polar]
to Cartesian co-ordinates (x, y, z) is given by
x = r cosθ sinφ (2.9)
y = r sinθ sinφ (2.10)
Fig. 2.5 Determination of location of a point on spherical co-ordinate system
2.2 Types of Co-ordinate System 55
z = r cosφ (2.11)
Again, the inverse relation indicates
r =
√
x2 + y2 + z2 (2.12)
θ = tan−1
( y
x
)
(2.13)
φ = tan−1
(√
x2 + y2
z
)
= cos−1
( z
r
)
(2.14)
2.3 Selection of Scale in Constructing a Graph
While constructing a graph, the selection of scale should be done carefully keeping
two things in mind: (i) the nature and range of the entire data set and (ii) the size of
the graph paper. Conventionally, the independent variable is shown along the x-axis
(abscissa) while the dependent variable is shown along the y-axis (ordinate). It is
not mandatory to make the scale of the x-axis and y-axis identical. In time series
data, the scale of the x-axis starts from the lowest value of the given variable or the
starting time of the time series, whereas the scale of the y-axis starts from the value
zero (0). But in the case of frequency distribution, the scale along the y-axis starts
from zero while the scale along the x-axis may start from zero or with the value
one point before the lowest value of the measured variable (Saksena 1981). After
selecting the suitable scale, all the points are plotted on the graph paper and then the
obtained points are joined by straight lines but it is not mandatory. Though several
types of graphs are there, the selection of suitable graph mainly depends on the type
and nature of data and the objectiveof the study or research.
In geographical research, the collected, classified, tabulated and summarized data
are represented graphically to make them easily understandable and comprehensive.
As most of the graphical representation of geographical data is done by geometrical
methods, thus it is also known as the geometrical representation of data.
2.4 Advantages and Disadvantages of the Use of Graphs
Graphical representation of various geographical data possesses some advantages as
well as some disadvantages:
Advantages
56 2 Representation of Geographical Data Using Graphs
1. Graphical representation is more attractive and appealing to the eyes, which
leaves an enduring impression on the mind and is thus easily understandable to
all.
2. The trend and tendency of the values of geographical variables (time series data)
can be easily understood.
3. It is very effective and useful to understand the nature and characteristics of
complex geographical data sets.
4. It helps in making a comparison of two or more sets of geographical data.
5. The relationship between several sets of geographical variables can be effec-
tively shown by this method.
6. Any type of inaccuracy and error in geographical data becomes perceptible by
their graphical representation.
7. It is useful for the interpolation of values of geographical variables.
8. Median, mode, quartile and other descriptive statistics can be easily calculated
and estimated by graphical representation of geographical data.
Disadvantages
1. Overall and detailed information of geographical data cannot be obtained from
their graphical representation.
2. It reveals only the approximate position; it seldom reflects the perfect values.
3. It is time-consuming to prepare the graph.
4. Selection of inappropriate graph may lead to erroneous conclusions and
decisions.
5. A high degree of variability between the values of geographic data may obstruct
the purpose of graphical representation.
6. Representation and understanding of several numbers of geographic variables
become difficult in the graph.
7. Sometimes the graph shows the difficulty to understand the inefficient, illiterate
and common people.
2.5 Types of Graphical Representation of Data
Graphical representation of data can be broadly classified into the following heads
given in Table 2.1.
2.5.1 Bi-axial Graphs or Line Graphs or Historigram
The values of two geographical elements or variables are represented along the sets
of ‘X’ and ‘Y ’ axes on a reference frame. The line graphs are generally drawn to
represent the time series data like temperature, rainfall, birth rates, death rates, growth
of population etc.
2.5 Types of Graphical Representation of Data 57
Table 2.1 Types of graphs
The values of different geographical variables change over time. A series of
observations recorded in accordance with the time of occurrence is called time series
data. The graphical representation of classified and summarized time series data is
called historigram in which time is considered as independent variable and the corre-
sponding geographical values are taken to be dependent variable. For the comparison
of temporal changes of two or more variables expressed in the same unit of measure-
ment, two or more historigrams are drawn. There are numerous geographical data
which can effectively and successfully be represented by historigram.
Time series graph or historigram indicates two important facts of geographical
data:
(1) Measurement and analysis of the changes of uni-variate geographical data.
(2) Comparison of changes of two or more geographical variables.
For the construction of historigram, time (year,month, day etc.) is shown along the
‘X’-axis and the corresponding geographical variable (temperature, rainfall, number
of landslide hazard, volume of water discharge in a river, number of population,
volume of population migration, amount of agricultural or industrial production etc.)
is shown along the ‘Y ’-axis following a suitable scale. Plotting of the values of any
geographical phenomenon or event with respect to time provides some points which
are then joined by a line called line graph or historigram (Figs. 2.6 and 2.7).
For example, the increase of population in Kolkata Urban Agglomeration (KUA)
with the advancement of time (Table 2.2) can be represented by historigram. Here,
different years are shown on the ‘X’-axis and the total population are shown on the
‘Y ’-axis and then the plotted points are joined by a line (Fig. 2.6).
Similarly, the variation of rice production in different years (Table 2.3) can be
represented by historigram. Here, different years are shown on the ‘X’-axis and the
amount of production of rice are shown on the ‘Y ’-axis and then the plotted points
are joined by a line (Fig. 2.7).
58 2 Representation of Geographical Data Using Graphs
Fig. 2.6 Line graph (Historigram) showing the temporal changes of total population in Kolkata
Urban Agglomeration (KUA) Source Census of India
Fig. 2.7 Line graph or Historigram (Production of rice in India, 2000–2011) Source Directorate
of Economics and Statistics (Government of India)
2.5.1.1 Open Line Graph
Simple Line Graph
When the line graph represents the values of only a single variable or element or
fact, then it is called a simple graph.
Arithmetic Graph
Use of arithmetic or linear scale on the horizontal (X-axis) and vertical (Y-axis)
axes to represent geographical data using line graph is more frequent and common.
2.5 Types of Graphical Representation of Data 59
Table 2.2 Data for line graph
or historigram (Temporal
change of total population in
Kolkata Urban
Agglomeration)
Year Total population (in millions)
1901 1.51
1911 1.74
1921 1.88
1931 2.14
1941 3.62
1951 4.67
1961 5.98
1971 7.42
1981 9.19
1991 11.02
2001 13.21
2011 14.03
Table 2.3 Data for line graph
or historigram (Production of
rice in India, 2000–2011)
Year Production of rice (million tons)
2000–01 84.98
2001–02 93.34
2002–03 71.82
2003–04 88.53
2004–05 83.13
2005–06 91.79
2006–07 93.36
2007–08 96.69
2008–09 99.18
2009–10a 89.13
2010–11b 80.41
aFourth advance estimates as released on 19.07.2010
bFirst advance estimates as released on 23.09.2010
Source Directorate of Economics and Statistics (Government of
India)
On an arithmetic scale, equal amounts or values are represented by equal distances,
i.e. the values of a data series plotted on an arithmetic scale increase or decrease at
a constant rate (even spaces between numbers). Thus, the distance from a value of
1 to 2 (distance is 1) is equal to that of the distance from 2 to 3 (distance is 1), 3
to 4 (distance is 1), 4 to 5 (distance is 1) and so on (Fig. 2.8a). Representation of
data on an arithmetic or a linear scale would produce a curving line, descending at a
declining (getting lower) angle for a diminishing series of values and ascending at a
rising (getting higher) angle for a growing series of values.
The major advantages and disadvantages of using arithmetic graphs are:
60 2 Representation of Geographical Data Using Graphs
Fig. 2.8 a Arithmetic scale on both the axes, bArithmetic scale on the ‘X’-axis but the logarithmic
scale on the ‘Y ’-axis, c Arithmetic scale on the ‘Y ’-axis but the logarithmic scale on the ‘X’-axis,
and d Logarithmic scale on both the axes
Advantages
(1) Presentation of geographical data with a line graph on arithmetic scales is very
easy and simple because basic mathematical principles are applied.
(2) Arithmetic line graphs are very easy to read and understand.Most of the readers
expect a level twice as high to be twice as large.
(3) Zeroes or negative values can be easily represented on arithmetic scales.
(4) These graphs are useful for the representation and understanding of the absolute
changes of values of geographical variables.
2.5 Types of Graphical Representation of Data 61
Disadvantages
(1) These graphs only show the absolute changes of values; however, these do not
show the relative changes. Thus,these are not useful for comparing the relative
changes (percentage) of values of geographical variables.
Logarithmic Graph
Representation of geographical data with a line graph on a logarithmic scale (equal
scale between powers of 10) is an alternative andmore useful technique in comparing
the rate of change of values. These graphs aremore useful and effective to understand
and compare the relative changes (percentage) of a set of values rather than their
absolute amounts of changes. Log-graph is commonly used when the range of values
of the variable is very large and an increase or decrease of the values occurs roughly
at a constant ratio. On a logarithmic scale, equal distances stand for equal ratios. For
instance, the distance from 1 to 2 is equal to that from 2 to 4
(
2
4 = 1
2
)
, 4 to 8
(
4
8 = 1
2
)
,
8 to 16
(
8
16 = 1
2
)
and so on at each interval, in the ratio 1:2 (vertical axis of Fig. 2.8b,
horizontal axis of Fig. 2.8c and both axes of Fig. 2.8d). Representation of data on
a logarithmic scale clearly depicts the percentage increase or decrease between two
data values.
In log-graph paper, the axes (either X-axis or Y-axis or both) are divided into
several parts of equal length, known as cycles. A single cycle corresponds to a
tenfold increase of values of variables, and similarly, two cycles indicate the 100-
fold increase of values. The value at the top of the first cycle is ten times more than
that of the value at the bottom of it and the value at the top of the second cycle is
ten times more than the value at the bottom of the second cycle (the top of the first
cycle), i.e. hundred times more than that of the value at the bottom of the first cycle
(vertical axis of Fig. 2.8b, horizontal axis of Fig. 2.8c and both axes of Fig. 2.8d). It
is because of the principle that a common logarithm is a power to which 10 should
be increased to generate a specified number. Thus, 100 = 102, 1000 = 103 and the
logarithm of 100 and 1000 are 2 and 3, respectively, and so on. Log scale can never
start with zeroes or negative values, as log (0) = ∞ (infinity). So, any positive value
should be taken at the origin by the user. Based on the selection of logarithmic scale
(either on the X-axis or Y-axis or both the axes), log-graphs are of two types.
Semi-logarithmic Graph
A semi-logarithmic or semi-log line graph has one axis on a logarithmic scale (equal
scale between powers of 10) and another axis on an arithmetic or linear scale (even
spaces between numbers) (Fig. 2.8b, c). These graphs are useful for the data with
exponential relationships, or where a single variable covers a large range of values. A
set of geographical data plotted using a logarithmic scale on the y-axis will resemble
a straight line, slanting up or down based on the nature of the data values. When the
values increase or decrease at a constant rate, it will appear as a straight line.
62 2 Representation of Geographical Data Using Graphs
Table 2.4 Database for
arithmetic and logarithmic
line graph (Age and
sex-specific variation of death
rates)
Age group Number of deaths (per year)
Male Female
<15 15 20
15–19 17 20
19–24 23 24
25–29 27 45
30–34 33 105
35–39 60 210
40–44 110 318
45–49 235 480
50–54 470 625
55–59 820 820
60–64 1340 1205
65–69 2110 1508
70–74 2905 1750
75–79 3380 1820
80–84 3385 2010
84+ 2000 1325
Log–Log Graph
In log–log graph, both the X (horizontal) and Y (vertical) axes are represented using
the logarithmic scale in which equal distances measure equal ratios (Fig. 2.8d).
The given two line graphs (Figs. 2.9 and 2.10) show the difference between the
two scales when representing the same data, i.e. age-specific number of deaths of
the male and female population (Table 2.4). The first line graph (Fig. 2.9) has been
drawn using the arithmetic scale on both axes. The graph demonstrates that female
death rates are slightly or little higher than the male death rates until about age
group 50–54. In the age group 55–59, the male death rate has started to exceed the
female death rate and in the age group 65–69, the rate becomes much higher and
staysmuch higher. However, the second line graph (Fig. 2.10) has been drawn using a
logarithmic scale on the ‘y’-axis. In this graph, the female death rates for the younger
age groups appear somewhat higher in comparison to the male death rates and the
relative (percentage) differences in the death rates for the older age groups are not
as higher as apparent in the arithmetic line graph.
So, the logarithmic graph highlights a possible significant difference between the
death rates of the male and female population in the younger age groups, whereas
this difference has been lost in the arithmetic line graph because of the plotting of
the higher absolute values for the older age groups.
2.5 Types of Graphical Representation of Data 63
Fig. 2.9 Arithmetic graph (Number of male and female deaths per year)
Fig. 2.10 Logarithmic graph (Number of male and female deaths per year)
Advantages and Disadvantages of Using Logarithmic Graph
Advantages
64 2 Representation of Geographical Data Using Graphs
(1) Logarithmic line graphs show the relative changes, i.e. these graphs are useful
to identify and understand the relative changes (percentage) of values of
geographical variables.
(2) In terms of comparative study, the logarithmic line graphs provide a more
complete depiction and explanation of the relationship that exists between sets
of data.
Disadvantages
(1) Representation of zeroes or negative values on logarithmic line graphs is not
possible. Also, these graphs are not so easy to construct like arithmetic graphs.
(2) Since most of the readers and users expect a level twice as high to be twice as
large, these types of graphs may be misleading to them because they do not
understand what type of comparison is shown in graphs.
(3) These types of graphs look very technical and discourage the readers and users
to try to recognize and explain these graphs.
Because of the aforementioned problems and difficulties, though logarithmic
line graphs provide a more complete depiction and explanation of the relationship
between series of data, these graphs are not widely recommended and used to repre-
sent geographical data. These graphs are not suitable to display the geographical
data in those fields and reports where common people are the targeted audience.
These graphs are excellent for specialized purposes and are for audiences having
adequate technical knowledge. In comparison, arithmetic line graphs are commonly
and frequently used for the representation of geographical data because these graphs
are simple and easy to understand.
Difference Between Arithmetic (Linear) and Logarithmic Line Graphs
The major differences between arithmetic and logarithmic line graphs are:
Arithmetic line graph Logarithmic line graph
1. Arithmetic or linear scale is used on both the
axes, i.e. on the X-axis (horizontal) and Y-axis
(vertical) to represent the data
1. Logarithmic scale is used either on the X-axis
(horizontal) or Y-axis (vertical) or both axes to
represent the data
2. Arithmetic line graph can be used to
represent any type of geographical data
2. Logarithmic line graph is commonly used
when the range of values of the data set is very
large
3. On an arithmetic scale, equal distances
represent equal amounts or values, i.e. the
values of a data series plotted on an arithmetic
scale increase or decrease at a constant rate
3. On a logarithmic scale, equal distances
represent equal ratios, i.e. the values of a data
series plotted on a logarithmic scale increase or
decrease at a constant ratio
4. Zeroes or negative values can be easily
represented on arithmetic line graphs
4. Representation of zeroes or negative values
on logarithmic line graphs is not possible
(continued)
2.5 Types of Graphical Representation of Data 65
(continued)
Arithmetic line graph Logarithmic line graph
5. Representation of data on an arithmetic
scale would producea curving line,
descending at a declining (getting lower) angle
for a diminishing series of values and
ascending at a rising (getting higher) angle for
a growing series of values
5. A set of data plotted using a logarithmic scale
on the y-axis will resemble a straight line,
slanting up or down based on the nature of the
data values. When the values increase or
decrease at a constant rate, it will appear as a
straight line
6. Arithmetic line graphs are very easy to read
and understand to the common people because
basic mathematical principles are applied
6. These types of graphs look very technical and
create difficulties to understand to the common
people. They are excellent only for the
specialized audiences having adequate technical
knowledge
7. These graphs only show the absolute
changes of values but not the relative changes.
Thus, these are not useful for comparing the
relative changes (percentage) of values of
geographical variables
7. Logarithmic line graphs provide a more
complete depiction and explanation of the
relationship between sets of data. These graphs
are useful to identify and understand the relative
changes (percentage) of values
Composite or Compound Line Graph
Sometimes the line graph shows the relationship between two or more than two
variables or elements or facts called composite or compound graph.
Poly Graph
Poly graph is a multiple line graph in which two or more sets of variables are repre-
sented by distinctive lines (Fig. 2.11). It is frequently used for immediate compar-
ison between several sets of variables, for instance, the death rates and birth rates
of different states in a country; male and female literacy rate in different census
years in a country (Table 2.5); proportion (%) of child, adult and old population in
different census years in a country; amount of production of different crops (rice,
wheat, maize, pulses etc.) in different years in a region etc. Generally, different vari-
ables are represented by different line patterns like a straight line (___), dotted line
(……), broken line (- - -) or line of various colours (Fig. 2.11).
Band Graph
A band graph is practically a standard and aggregate line graph which shows the
trends of values in percentage or numbers or quantity for successive time periods
in both the total and its component parts (Table 2.6) by a series of lines drawn
on the same frame (Fig. 2.12). Band graph shows how and in what proportion the
component items constituting the aggregate are distributed. Different component
items are represented one above the other and the intervening gaps between the
66 2 Representation of Geographical Data Using Graphs
Fig. 2.11 Poly graph showing total, male and female literacy rates
Table 2.5 Worksheet for poly graph (Total, male and female literacy rates in different census years
in India)
Census year Literacy rate (%) Scale selected Literacy rate according to
scale (cm)
Total Male Female Total Male Female
1901 5.35 9.83 0.60 1 cm to 10% literacy
rate
0.53 0.98 0.06
1911 5.92 10.56 1.05 0.59 1.06 0.1
1921 7.16 12.21 1.81 0.72 1.22 0.18
1931 9.5 15.59 2.93 0.95 1.56 0.29
1941 16.1 24.9 7.30 1.6 2.5 0.73
1951 16.67 24.95 7.93 1.7 2.5 0.79
1961 24.02 34.44 12.95 2.4 3.4 1.29
1971 29.45 39.45 18.69 2.9 3.9 1.87
1981 36.23 46.89 24.82 3.6 4.7 2.48
1991 42.84 52.74 32.17 4.3 5.3 3.2
2001 54.51 63.23 45.15 5.4 6.3 4.51
2011 64.32 71.22 56.99 6.4 7.1 5.7
Source Census of India
successive lines are filled by different colours or shades so that the graph looks like
a series of bands (Fig. 2.12). When the differences in values in component parts
are small, then the band graph becomes impressive representing the trends of their
distribution but when the variations are too large then the band graph becomes less
2.5 Types of Graphical Representation of Data 67
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68 2 Representation of Geographical Data Using Graphs
Fig. 2.12 Band graph showing the production of various crops in different years in India Source
Directorate of Economics and Statistics, Ministry of Agriculture and Farmers Welfare
impressive and its legibility and clarity is marred. In the geographical study, band
graph is useful for different purposes, including dividing the total crop production
into different crops, total cost into component costs, total production by type of
commodity or industries and other such relationships.
2.5.1.2 Closed Line Graph
Climograph
The concept and the idea of climograph was first conceived by J. Ball in the form
of ‘Climatological Diagrams’ (Singh and Singh 1991) and it was introduced by
Griffith Taylor in the first half of the twentieth century (1949). The variations of
world climatic conditions were summarized by Koppen using this graph. Again, J.B.
Leighly explained the idea of Koppen to compare the climatic conditions of different
parts of the world. Additionally, another two important types of climograph were
2.5 Types of Graphical Representation of Data 69
Fig. 2.13 USDA type of climograph
designed by the United States Department of Agriculture (U.S.D.A., 1941) and E.E.
Foster (1944). The climograph was actually devised to show the scale of habitability
for white settlers within the tropics.
Climograph of USDA Type (1941)
TheUnited States Department of Agriculture devised a type of climograph in 1941 in
whichmeanmonthlywet-bulb temperatures (°F) is plotted againstmeanmonthly dry-
bulb temperatures (°F) on a referenced frame. Twelve points, each for one month, are
obtained on the graph paper and the joining of these points results in a closed 12-sided
polygon called climograph. Generally, this type of climograph is depicted to explain
the climatic conditions with respect to human physiological comfort (Fig. 2.13).
Climograph of Foster Type (1944)
In 1944, E.E. Foster devised a type of climograph in which mean monthly tempera-
tures (°F) is plotted against those of monthly precipitation (inches) on a referenced
70 2 Representation of Geographical Data Using Graphs
Fig. 2.14 The base frame of Foster’s climograph
frame.Monthly precipitation (rainfall) is shown along the ‘X’-axis (abscissa), gradu-
ated from 0 to 18 inch and the meanmonthly temperature is shown along the ‘Y ’-axis
(ordinate), graduated from −20 to 100 °F (Fig. 2.14).
The reference frame has been divided into six temperature zones from bottom
to top, namely frigid zone (−20–0 °F), cold zone (0–32 °F), cool zone (32–50 °F),
mild zone (50–65 °F), warm zone (65–80 °F) and hot zone (more than 80 °F).
Additionally, the top four zones are divided into five sub-zones based on the amount
of precipitation, namely arid zone (0.32–1.03 inch), semi-arid zone (0.59–1.93 inch),
sub-humid zone (1.10–3.60 inch), humid zone (2.05–6.73 inch) and wet zone (more
than 2.05 inch and more than 6.73 inch) (Fig. 2.14). Each month is depicted by a
letter symbol and the joining of these points results in a closed 12-sidedpolygon
called climograph. This type of climograph is primarily used to depict the climatic
classification system proposed by C.W. Thornthwaite.
Climograph of G. Taylor (1949)
According to G. Taylor, climograph is a 12-sided polygon obtained from the graph-
ical representation of wet-bulb temperature (°F) and the relative humidity (%) of
12 months of a particular place or station it corresponds to (Fig. 2.15 and Table 2.7).
The relative humidity is shown along the ‘X’-axis (abscissa), graduated from 20 to
100% and the wet-bulb temperature is shown along the ‘Y ’-axis (ordinate), gradu-
ated from −10 to 90 °F. The 12 points (each for a month) are obtained on the graph
paper by plotting wet-bulb temperature against relative humidity for 12 months and
2.5 Types of Graphical Representation of Data 71
Fig. 2.15 Climograph showing the wet-bulb temperature and relative humidity of Kolkata (after
G. Taylor)
Table 2.7 Monthly wet-bulb temperature (°F) and relative humidity (%) of Kolkata, West Bengal
Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Wet-bulb
temperature (°F)
64.7 68.5 70.5 79.8 82.9 82.4 80.8 82.6 80.4 78.1 68.9 68.5
Relative
humidity (%)
41 45 40 39 59 67 83 80 76 70 46 49
joining of these points results in a 12-sided polygon called climograph. He marked
four corners in the framework demonstrated by Keen (SW), Raw (SE), Muggy (NE)
and Scorching (NW) (Fig. 2.15).
(a) Keen: Low wet-bulb temperature (below 40 ◦F) and low relative humidity
(below 40%).
(b) Raw: Low wet-bulb temperature (below 40 ◦F) and high relative humidity
(above 70%).
(c) Muggy: High wet-bulb temperature (above 60 ◦F) and high relative humidity
(above 70%).
(d) Scorching: Highwet-bulb temperature (above 60 ◦F) and low relative humidity
(below 40%).
He also designed a tentative scale of discomfort and identified six categories
regarding it:
(1) Very rarely uncomfortable: below 45 °F (40–45 °F)
72 2 Representation of Geographical Data Using Graphs
Table 2.8 Mean monthly temperature and rainfall of Burdwan district, West Bengal
Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean
temperature
(°C)
19.3 21.7 26.1 29.7 31.7 30.2 29.6 29.1 28.4 28.2 24.1 18.6
Rainfall
(cm)
0.54 2.12 8.54 8.93 9.26 24.1 23.8 36.53 23.7 6.74 2.52 0
(2) Ideal: 45–55 °F
(3) Rarely uncomfortable: 55–60 °F
(4) Sometimes uncomfortable: 60–65 °F
(5) Often uncomfortable: 65–70 °F
(6) Usually uncomfortable: above 70 °F (70–75 °F).
The graph shifting towards the corners indicates the discomfortable characteristics
of the climate. ‘Scorching’ and ‘Keen’ zones represent the hot desert and cold climatic
characteristics, respectively,whereas the ‘Muggy’ region indicates the tropical humid
climate (Fig. 2.15). The shape of the climograph is useful to understand the climatic
character of a place or station. It is very simple and easy to compare the unknown
climates with reference to the shape of the typical climograph (Singh and Singh
1991).
• Spindle-shaped climograph indicates the dry continental climate.
• Diagonal climograph represents the Mediterranean type of climate.
• Diagonal elongated climograph indicates the monsoon type of climate.
• Full-bodied climograph represents the ideal British type of climate.
Hythergraph
Hythergraph, a special form of climograph, was devised by Taylor (1949) to show
the relationship between mean monthly temperature and mean monthly rainfall. It
is drawn in the same way as in the case of climograph. Mean monthly rainfall is
represented along the ‘X’-axis (abscissa) and mean monthly temperature is shown
along the ‘Y ’-axis (ordinate). The 12 points (each for a month) are obtained on
the graph paper by plotting mean monthly temperature against mean monthly rain-
fall for 12 months and joining of these points results in a 12-sided polygon called
hythergraph. Table 2.8 shows themeanmonthly temperature and rainfall of Burdwan
district, West Bengal and these data are graphically represented using a hythergraph
(Fig. 2.16).
2.5 Types of Graphical Representation of Data 73
Fig. 2.16 Hythergraph showing the mean monthly temperature and rainfall of Burdwan district
Significance of Hythergraph
1. Hythergraph is principally used for comparing the climatic characteristics of
different regions as affecting the cultivation of various crops, like rice, wheat,
pulses, cotton etc.
2. It summarizes the basic climatic differences with respect to human activity,
specifically in the context of settlement.
2.5.2 Tri-axial Graphs
Values of three geographical things or elements are represented along the sets of ‘X’,
‘Y ’ and ‘Z’ axes on a reference frame. These graphs are very useful to represent
three inter-related variables.
74 2 Representation of Geographical Data Using Graphs
2.5.2.1 Ternary Graph
A ternary graph is an equilateral triangular graph that displays the proportion of
three inter-related components or variables that sum to a constant (100%). Three
components or variables are shown along three sides of the triangle, respectively.
Each side of the triangle is graduated from 0 to 100% to represent tri-component
data. The vertices of the triangle are given by (1, 0, 0), (0, 1, 0) and (0, 0, 1), i.e. each
apex forms 0% on two scales and 100% on the third (Fig. 2.17).
Techniques and Principles of Representation of Data in Ternary Graph
Ternary graph becomes very useful whenever the data composed of three inter-
related components or variables can be converted into percentages totalling 100.
In this graph, data are represented by using barycentric co-ordinates (barycentric
Fig. 2.17 Identification of position of points in ternary graph
2.5 Types of Graphical Representation of Data 75
Table 2.9 Database for
ternary graph (Proportion of
sand–silt-clay in sediments)
Stations Proportion of sediment particles (%)
Sand Silt Clay
Kolaghat 68 25 7
Soyadighi 65 17 18
Anantapur 52 30 18
Pyratungi 60 12 28
Dhanipur 45 35 20
Geonkhali 54 16 30
co-ordinates are triples of numbers [x1, x2, x3]) corresponding to amounts placed at
the vertices of a reference triangle (say �ABC). These amounts then determine the
location of a point ‘P’, which is the geometric centroid of the three amounts and is
identified with co-ordinates (x1, x2, x3) (Fig. 2.17).
Since the values of three components all add up to 100%, all three values are
plotted on the graph as a collection of points. The position of points within the
triangular graph reflects the relative dominance of each component (Fig. 2.17).
Example
Data like age composition (young, adult and old), textural composition of soil or sedi-
ment (sand, silt and clay), occupational structure of population (primary, secondary
and tertiary) etc. are suitable for representation in ternary graph.
Table 2.9 shows the proportion of sand, silt and clay in the sediment samples
collected from the bed of Rupnarayan River at different sites (Kolaghat, Soyadighi,
Anantapur, Pyratungi, Dhanipur and Geonkhali) and it is represented graphically
in a ternary graph (Fig. 2.18). Types of sediment samples are easily understood by
observing the location of points in the ternary graph.
A ternary graph was, however, found the most appropriate technique for the
classification of a large number of Indian towns. Asok Mitra (1964) for the first
time used the ternary graph for functional classification of towns in the 1961 census.
His method of classification is based on the concept of dominant functions of a
city. The seven census categories of workers were grouped into three broad non-
agricultural categories, namely (1) industry, (2) trade and transport and (3) services.
The percentages of three categories of towns are then plotted on a ternary graph and
their position in the triangle was taken as the main determinant of their functional
classification.
76 2 Representation of Geographical Data Using Graphs
Fig. 2.18 Identification of sediment type using ternary graph
2.5.3 Multi-axial Graphs
The reference frame is composed of a network of evenly spaced linesradiating from
the centre. The radiating lines are drawn at true azimuth on vector graph. Values are
plotted along the radiating lines and the obtained points are then joined.
2.5.3.1 Radar or Spider or Star Graph
A radar graph, also called spider graph or star graph, is the graphical representation
of the multivariate data (three or more variables) in the form of a two-dimensional
graph consisting of a sequence of equi-angular spokes or axes starting from the same
point called radii, each representing a different variable. The length of each spoke
is proportional to the quantity of the variable for the data point with respect to the
maximum quantity of the variable across all data points. The spokes are then joined
with a line of a selected colour or pattern in the form of a shaded polygon to represent
each category, creating a star-like shape with points equal to the number of categories
(Fig. 2.19).
A radar graph provides the user with numerous visual comparisons by portraying
multivariate data with different variables. In other words, if we want to understand
2.5 Types of Graphical Representation of Data 77
Fig. 2.19 Radar graph
(Production of different
crops)
how multiple data points interact with each other and make a comparison against
another set of multiple data points, then a radar graph is one of the best ways.
This graph is mainly drawn to display the continuous diurnal, monthly or annual
rhythm of different geographic variables. For example, hourly data of atmospheric
humidity, atmospheric temperature, sunshine and soil temperature; monthly data of
atmospheric humidity, rainfall, atmospheric temperature; and yearly data of produc-
tion of different crops, industrial goods etc. can be easily represented in a radar
graph.
Methods of Construction
1. A suitable scale is at first selected to represent the data, and the required number
of concentric circles is drawn at regular intervals (Fig. 2.19).
2. The required number of equi-angular radial straight lines (axes) of corre-
sponding lengths is drawn from the centre (i.e. the point of origin). Each axis
shares the same divisions and scale, but the method in the range of variable
values maps to this scale may be different between the represented variables.
3. The values from a single observation are represented along each axis and joined
to form a polygon to make the graph more easily readable and understandable
(Fig. 2.19).
4. More number of observations can also be placed in a single graph with the help
of multiple polygons.
78 2 Representation of Geographical Data Using Graphs
Table 2.10 Data for radar graph (Production of different crops in different years)
Year Production of different crops (tonne)
Grains Pulses Vegetables Cereals
2007 850 1143 885 847
2008 1284 691 1295 980
2009 1170 680 1409 1272
2010 974 1182 599 1310
2011 554 1405 972 1354
2012 1491 453 937 568
2013 820 572 1085 1004
2014 584 439 802 885
2015 1319 762 974 726
2016 1270 1277 1214 815
5. Overlay these polygons and adjust the opacity of every polygon for each of the
observations. Hence, an hourly graph is represented by a 24-sided polygon and
a monthly graph by a 12-sided polygon.
Steps of Drawing Radar Graph in Microsoft Excel
Step 1: Insert the data in a suitable format.
Step 2: Go to Insert tab → Other Charts → Select Radar with Marker Chart. A
blank radar graph will be inserted.
Step 3: Right click on the blank graph and click on select data.
Step 4: Click on Add button
Step 5: Select Series name as Grains (for the following example) and Series value
as production values (Table 2.10) and click Ok.
Step 6: Repeat the same procedure for all the remaining data. After this, click on
Ok and a graph will be inserted (Fig. 2.19).
Step 7: Format the graph according to your need.
How to Understand the Radar Graph
Like the column or bar graph in the spider graph we also have ‘X’ and ‘Y ’ axes. The
X-axis is nothing but the extreme end of the radial line (spider) and each step of the
radial line is considered as Y-axis. Zero (0) point of the radar graph starts from the
centre of the wheel. Towards the margin of the spike, a point arrives, and the higher
is the value.
2.5 Types of Graphical Representation of Data 79
Interpretation of the Graph
• By having a look at the spider graph (Fig. 2.19) we can understand that in 2012
the production of grains was the highest among all the 10 years productions. In
2011, the production of grains was the lowest.
• In the case of pulses, the highest productionwas in 2011 and the lowest production
was in the year 2014.
• In the case of vegetables, the highest production was in the year 2009 and the
lowest production was in 2010.
• In the case of pulses, the highest production was in the year 2011 and the lowest
production was in the year 2012.
Advantages of Using Radar Graph
Radar or spider graphs are frequently used in the geographical analysis for the
comparison of the distributions along the radial lines of different directions of
frequency and index data to compare two or more areas. The major advantages
of using this graph are as follows:
1. The radar graph is more suitable when the absolute values aren’t critical for a
user but the whole graph tells some story.
2. Radar graphs are very useful for strikingly showing outliers and commonality,
or when one graph is larger in every variable than another.
3. Several attributes become easily comparable, each along their own axis, and
their overall variations are clear by the shape and size of the drawn polygons.
4. In radar graph, many variables can be easily shown next to each other whilst
still giving each variable the identical resolution.
5. Radar graphs are more effective when there is the need to compare the perfor-
mance of one thing to a standard or a group’s performance. For example, if one
has a radar graph portraying data about the average quantity of production of
crops in different regions, one could easily superimpose another polygon repre-
senting a particular crop production data in order to quickly observe how that
crop compares to average crop production in each region (Fig. 2.19).
Limitations
The major disadvantages of this graph are:
(1) The comparison of data on a radar graph becomes difficult once there are more
than two webs on the graph.
(2) When too many variables are represented along different axes, it creates the
crowding of data.
(3) Though there are several axes which have gridlines joining them for indication,
problems arise when observers seek to compare the values along different axes.
80 2 Representation of Geographical Data Using Graphs
(4) Each axis of a radar graph shares a common scale, which means that the range
of values of each variable requires to be mapped based on this shared scale in
a different way. The way of mapping these variables is not understandable in
most cases, and can even be misleading.
(5) Another important problem is that observers could potentially think that the
area of the polygons is a very important thing to consider. But, the shape and
area of the polygons can vary largely based on how the axes are placed around
the circle.
Alternatives to radar graphs are bar graphs and parallel coordinate graphs.
2.5.3.2 Polar or Rose Graphs
A polar or rose graph is the graphical representation of the direction as well as
magnitude or quantity of different phenomena or variables, especially geographical
in nature. Phenomena or variables characterized by direction and distance from a
specific point of origin can be plotted on polar graphs (Figs. 2.20 and 2.21). They
are analogous to radar graphs, but as a substitute for any variable. They exclusively
emphasize geographical phenomena.
Fig. 2.20 Wind rose graph
showing the percentage of
days wind blowing from
different directions
2.5 Types of Graphical Representation of Data 81
Fig. 2.21 Polar graph
showing the number of
corries facing towards
different directions
Principles and Methods of Construction
In polar or rose graph,values are plotted as radii from a point of origin (pole) with
the help of a polar coordinate system. This graph draws the ‘X’ and ‘Y ’ co-ordinates
in each series as (theta [θ], r) (discussed in types of co-ordinate section), where
theta is the amount of rotation from the origin (vector angle) and ‘r’ is the distance
from the origin (radius vector). The outer values in the circle always represent the
degrees in the circle. Data ‘X’ holds the x-axis position in degrees and data ‘Y ’ holds
the position of each phenomenon of the variable on the y-axis (Figs. 2.20 and 2.21).
These graphs are especially useful where vector values are involved.
Polar or rose graphs are useful for the analysis of various geographical data
containing magnitude and direction values. These graphs are generally used to repre-
sent the direction, magnitude and frequency of ocean or wind waves, the direction
of facing of cirques or corries, the orientation of the long axes of pebbles or boulders
etc.
Wind rose graph is the most frequently used polar graph in geographical analysis.
Meteorologists, climatologists and geographers use wind rose to graphically display
wind speed and wind direction at a particular location over a defined observation
period (Table 2.11 and Fig. 2.20).Wind rose can be prepared for month-wise, season-
wise or yearly as required. It typically uses 16 cardinal directions, such as north (N),
north-east (NE), south (S), east (E) etc., although they may be sub-divided into
as many as 32 directions. In terms of the measurement of angle in degrees, north
corresponds to 0°/360°, east to 90°, south to 180° and west to 270°.
Figure 2.20 shows the percentage of days wind blowing from different directions.
It is clear from the graph that only 6% of winds are in a calm condition. About 29% of
82 2 Representation of Geographical Data Using Graphs
Table 2.11 Percentage of
days wind blowing from
different directions
Wind direction Percentage of days wind blowing from this
direction
North 29
North-east 7
East 10
South-east 12
South 10
South-west 9
West 4
North-west 13
Calm 6
Table 2.12 Data for
polar graph (The orientation
of corries in a glacial region)
Orientation of corries Number of corries facing towards this
direction
North 30
North-east 60
East 40
South-east 50
South 0
South-west 10
West 0
North-west 20
winds are blowing from the northerly direction, followed by 13% from north-west,
12% from south-east, 10% from south, 9% from south-west etc. So, there is enough
variability in the directions of wind blowing.
Table 2.12 and Fig. 2.21 show that most of the corries in the glacial region are
facing towards north, east and south-east directions. It is evident from the figure that
the faces of 60 corries are in the north-easterly direction, 40 corries are in the easterly
direction and 50 are in the south-easterly direction.
Advantages and Disadvantages of the Use of Polar or Rose Graph
Advantages
1. Multiple sets of data can be easily compared.
2. Lots of data can be represented on a single graph.
3. Easy to understand and interpret.
4. Individual components within the graph can be easily compared.
2.5 Types of Graphical Representation of Data 83
Disadvantages
1. Linking the data and statistical tests is difficult.
2. It is hard to spot anomalies.
3. Difficult to consider a suitable scale.
2.5.4 Special Graphs
2.5.4.1 Scatter Graph
Scatter graph is the simplest and easiest way to show the relationship between two
variables (bi-variate data) at a glance. Bi-variate data is the data that deals with the
simultaneousmeasurement of two variables that can change and are compared to find
the relationships. In bi-variate data, one variable is influenced by another variable
and thus bi-variate data has an independent (X) and a dependent variable (Y ) (Table
2.13). It is because of the fact that the change of one variable depends on the change
of the other. An independent variable is a part of data or condition in an experiment
that can be changed or controlled. A dependent variable is a part of data or condition
in an experiment that is affected or influenced by an external factor, most frequently
the independent variable. Bi-variate data can be easily represented in a scatter graph
to understand the type and nature of co-relation that exists between them. In this
method, the independent variable is shown along the ‘X’-axis and the dependent
variable is shown along the ‘Y ’-axis. Scattered points are obtained by putting the
values of Y with respect to X. In case of a trend or correlation, a ‘line of best fit’ can
then be drawn within a scatter graph (Fig. 2.22).
For example, the relationship between height frommean sea level and the number
of settlements, the relationship between basin area and run-off etc. can be easily
represented using scatter graph.
Table 2.13 Database for
scatter graph (The
distributions of air
temperature in the month of
April around an urban area)
Distance from CBD (km) [X] Air temperature (°C) [Y]
1.3 41.25
3.7 41.02
5.2 40.39
7.1 39.87
9.7 39.58
11.5 39.01
17.5 38.09
18.2 37.73
21.7 35.25
25.7 32.80
84 2 Representation of Geographical Data Using Graphs
Fig. 2.22 Scatter graph
(Relation between the
distance from CBD and air
temperature)
Fig. 2.23 Positive, negative and no co-relation
The location and orientation of points in the scatter graph indicate the type and
nature of co-relation between variables.
Positive, Negative and Zero Co-relation
When the points are oriented from lower left to upper right then it indicates the
positive co-relation between the variables (Fig. 2.23a). Here, two sets of data or
variables steadily tend to move together in the same direction, i.e. an increase in the
value of one set of variables causes an increase in the value of another set of variables
and vice versa. For example, distances travelled and amount of transport cost, the
slope of land and rate of soil erosion, income and expenditure of a family etc. are
positively co-related. When the values of both the variables tend to move together in
the same direction with a constant proportion then it is known as a perfect positive
correlation. In this co-relation, all the plotted points lie on a straight line that rises
2.5 Types of Graphical Representation of Data 85
Fig. 2.24 Perfect positive and negative co-relation
from the lower-left corner to the upper-right corner. Numerically, it is indicated as
+1 (r = +1) (Fig. 2.24a).
On the other hand,when two sets of data or variables steadily tend tomove together
in the opposite direction, i.e. an increase in the value of one set of variables causes a
decrease in the value of another set of variables and vice versa, then it is called inverse
or negative co-relation (Fig. 2.23b). For example, height from mean sea level and
the number of settlements, distance from forest area and amount of organic matter in
the soil, price of a commodity and its demand etc. are negatively co-related. When
the values of both the variables tend to move together in the opposite direction with
a constant proportion, then it is known as perfect negative co-relation. In this co-
relation, all the plotted points lie on a straight line falling from the upper-left corner
to the lower-right corner. Numerically, it is indicated as −1 (r = −1) (Fig. 2.24b).
When one set of variables does not change even with the change of another set of
variables (change in one variable does not depends on the change of another variable),
then the relationship between them is called zero co-relation or non-co-relation, i.e.
no co-relation exists between variables (Fig. 2.23c). For example, marks in physics
and marks in geography, the height of persons and their intelligence etc.
Linear and Nonlinear or Curvilinear Co-Relation
Linear or nonlinear co-relation is a function of the constancy of change of ratio
between two variables. In linear co-relation, the amount of change in one variable
maintains a constant ratio to the amount of change in the othervariable, i.e. the ratio
of change of values between two variables is equal. The points obtained from the
plotting of the values of one variable with respect to the other on a graph will move
around a line (Fig. 2.25a).
In nonlinear or curvilinear co-relation, the amount of change of variables is not
constant, i.e. the ratio of change of values between two variables is unequal. The
points obtained from the plotting of the values of one variable with respect to the
other on a graph will move around a curve (Fig. 2.25b).
86 2 Representation of Geographical Data Using Graphs
Fig. 2.25 Linear and nonlinear co-relation
2.5.4.2 Ergograph
The term ‘ergograph’ was first used by Dr. Arthur Geddes of the University of
Edinburgh. An ergograph is a special kind of multivariate graph which represents
the relationship between season, climatic elements and cropping patterns (human
activities). Various stages of the cycle of plant growth, i.e. sowing, growing, flow-
ering, maturing, harvesting etc., intimately corresponds to seasonal characteristics of
weather conditions. Variation of seasons are manifested by different climatic char-
acters and cropping patterns. The time of maturity of different crops varies from one
another. Some crops are annual, some are bi-annual and somemay require only a few
months to be matured. Ergograph can be drawn either by the Cartesian co-ordinate
method (rectangular form) or by the polar co-ordinate method (circular form).
In the Cartesian co-ordinate method or rectangular form, different climatic
elements like mean monthly temperature, rainfall, relative humidity etc.
(Table 2.14) are marked along the ‘Y ’-axis (vertical axis) in the form of poly-
graphs. However, the monthly rainfall is generally represented by vertical bars. The
12 months are plotted along the ‘X’-axis (horizontal axis). Below the horizontal axis
(primary baseline), a crop calendar is drawn in the form of rectangles on a selected
scale to represent the acreage of different crops (Fig. 2.26 and Table 2.15). The
length of each rectangle must correspond to the growing season of the crop while
Table 2.14 Data for ergograph (Monthly temperature, relative humidity and rainfall of Howrah,
West Bengal)
Months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Temperature (°C) 16 18 30 32 33 30 28 28 27 25 19 17
Relative humidity (%) 51 48 54 60 65 78 80 81 75 70 57 49
Rainfall (cm) 1.5 5.3 7.8 6.9 12.4 22 23 34.3 24 7.5 3.9 0.8
2.5 Types of Graphical Representation of Data 87
Fig. 2.26 Ergograph showing the relationbetween seasons, climatic elements and croppingpatterns
of Howrah, West Bengal
the breadth of them will be directly proportional to the crop acreage based on the
selected scale. Again, each rectangle may be divided into different parts to indicate
the time periods of various stages of crops grown (Fig. 2.26).
88 2 Representation of Geographical Data Using Graphs
Table 2.15 Data for ergograph (Net acreage of different crops and their growing seasons ofHowrah,
West Bengal)
Crops Seasons Net acreage (,000)
Sowing Growing Harvesting
Aus April May to mid of
August
Mid of August to
September
200
Aman July to mid of
August
Mid of August to
October
November to
December
650
Boro Mid of November
to December
January to mid of
March
Mid of March to
mid of April
500
Jute April May to August September to mid of
October
120
Pulses Mid of October to
mid of November
Mid of November to
mid of February
Mid of February to
mid of March
220
Polar Co-ordinate or Circular Ergograph of A. Geddes and G.G. Ogilvie
(1938)
A. Geddes and G.G. Ogilvie (1938) developed polar co-ordinate or circular form
of ergograph to show the continuous rhythm of seasonal activities (Table 2.16) in
which 12months of a year aremarked around the circumference of the circle, forming
30° sectors (Fig. 2.27). Concentric curves are drawn to show the nature of activities
done each month and the amount of time (hours per day) assigned to each type of
activity. The time scale, ranging from 0 to 24 h per day, is a square root scale and is
represented along the radius of the circle (Fig. 2.27). This type of ergograph is also
popularly known as a polar strata graph or polar layer graph or polar line graph (as
the data form ‘bands’ on the graph).
2.5.4.3 Ombrothermic Graph
Climatic graphs summarize the trends in temperature and precipitation for no less
than 30 years. They are likely to establish the relationship between temperature
and precipitation and determining the span of dry, wet and extremely wet periods.
Ombrothermic graph, also called Walter Lieth graph, is an important climatic graph
used to compare the averagedryness andwetness of a place.Thedata ofombrothermic
graphmust be the average for no less than 30 years. This graphwas first designed and
used by French bio-geographer and naturalist, Marcel-Henri Gaussen to graphically
depict the mean monthly temperature and monthly precipitation of a place.
2.5 Types of Graphical Representation of Data 89
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90 2 Representation of Geographical Data Using Graphs
Table 2.17 Data for ombrothermic graph (Average temperature and rainfall of Purulia district,
West Bengal)
Months Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
Average rainfalls
(mm)
13 24 21 26 45 223 281 300 259 82 10 4
Average temperatures
(oC)
18.8 21.9 26.8 31.6 33.3 31.2 28.3 28.1 28 26.5 22.2 19.4
Fig. 2.27 Circular
ergograph showing the
rhythm of seasonal activities
(after A. Geddes and G.G.
Ogilvie 1938)
Principles and Methods of Construction
(1) The mean monthly temperature (°C) and monthly rainfall (mm) of
Purulia district, West Bengal (Table 2.17) have been represented by Ombroth-
ermic graph (Fig. 2.28). For the drawing of this graph, months of the year
are shown along the x-axis while one y-axis (y1) represents the mean monthly
temperature and another y-axis (y2) represents the total monthly precipitation.
(2) The x-axis of the graph should begin with the coldest month of the year. In
the case of the places located in the Northern Hemisphere, the x-axis should
start with January, whereas in the Southern Hemisphere, it should start with
the month of July.
(3) Mean monthly temperature and monthly precipitation should be expressed in
degree centigrade (°C) and millimetres (mm), respectively. The selection of
the scales (y1 and y2) is very important and it should follow the following
relationship:
2.5 Types of Graphical Representation of Data 91
Fig. 2.28 Ombrothermic graph of Purulia district, West Bengal
Temperature (T) = 1
2
× Precipitation (P)
For example, the mean monthly temperature of 5 °C on the y1-axis have to be
equal to 10 mm of total monthly precipitation on the y2-axis.
(4) The selection of scales on both the axes of this graph is based on the Gaussen-
Bagnouls Aridity Index (Sarkar 2015):
(i) Precipitation more than three times the temperature (P > 3 T) indicates
the wet period.
(ii) Precipitation between two times and three times of the temperature (3 T
> P > 2 T) indicates the semi-wet period.
(iii) Precipitation less than two times the temperature (P < 2 T) indicates the
arid or dry period.
(5) Generally, the precipitation and temperature curves are represented in blue and
red lines, respectively.
(6) When the precipitation curve lies below the temperature curvethen it indicates
a period of dry condition or xeric period, but if the precipitation curve lies
above the temperature curve then it indicates a period of wet condition. When
the precipitation curve exceeds 100mm then it signifies a period of an excessive
wet condition (Fig. 2.28).
92 2 Representation of Geographical Data Using Graphs
(7) The station name and its elevation should be mentioned in the top left, average
temperature and average rainfall in the top right, and extremes of temperature
in the second line should be shown.
Inference: The station has a dry span between November and May and a wet span
from June to October. Between the month of June and September, it is an excessive
wet period.
Demerits of this graph
The major demerits of this graph are as follows:
(1) It lays on a scale that applies only to the mid-latitude climates.
(2) It can be only constructed and read by using the metric system.
2.5.4.4 Water Balance or Water Budget Curve
In nature, water is almost in a constant motion due to the changes of its state from
liquid to solid or vapour in appropriate environments. Law of mass conservation
signifies that within a particular area for a specific period of time, the inflows and
outflows ofwater are equal, including any change of storage ofwater in the concerned
area, i.e. the water coming into an area has to depart the area or be stored within the
area. The supply of groundwater in an area indicates whether a stage is one of water
utilization, deficiency, recharge or surplus.
Water balance techniques are very important for the solution of various theoretical
and practical hydrological problems and disasters. This approach helps us to evaluate
the water resources quantitatively and their transformation due to the influence of
humanactivities.Detailed knowledge about thewater balance structure of river basins
and groundwater basins offers a platform to make various hydrological projects valid
for the control, redistribution and rational use of water resources with respect to time
and space (Sokolov and Chapman 1974).
Formulation of Water Balance Techniques
Techniques of water balance estimation can be formulated by the following
parameters and equations:
(A) Gains: Precipitation (P)
(B) Soil moisture recharge or storage (R)
(C) Losses: Utilization (U) and evapotranspiration
(a) Actual evapotranspiration (AE)
(b) Potential evapotranspiration (PE)
Simple water balance
1. Environments with abundant moisture condition
2.5 Types of Graphical Representation of Data 93
Table 2.18 Water need and supply (mm) of a region (field capacity: 100 mm)
Month Jan Feb Mar Apr May June Jul Aug Sep Oct Nov Dec
Supply of water
(mm)
125 105 117 128 125 96 82 81 80 72 102 103
Need of water
(mm)
6 12 33 66 108 149 170 156 113 63 20 12
Supply minus
need
+119 +93 +84 +62 +17 -53 -88 -75 -33 +9 +82 +91
Water budget
section
S S S S S U U/D D D R R R/S
P > PE, thus AE = PE
2. Environments with inadequate moisture condition
P < PE, thus AE < PE
3. Environments with seasonal moisture condition.
In seasonal moisture environments, calculation of the monthly water budget is
done based on the following parameters:
a. Precipitation (P)
b. Potential evapotranspiration (PE)
c. Actual evapotranspiration (AE)
d. Change in water storage (�ST)
e. Difference between P and PE (P − PE)
f. Deficiency of water (D)
g. Soil moisture storage up to field capacity (ST)
h. Surplus of water (S): After attaining field capacity (ST), excess precipitation
(P) is available as surplus.
A water balance equation is simply expressed as follows:
P = Q + E ± �ST (2.15)
where P is precipitation, Q is run-off, E is evaporation and �ST is the surface,
sub-surface and groundwater storage.
In seasonal moisture environments, in the annual cycle of water balance estima-
tion, a period of soil moisture recharge (R) is followed by a period of water surplus
(S), and subsequently, a period of soil moisture utilization (U) is followed by a
period of water deficiency (D) (Sutcliffe et al. 1981) (Table 2.18). The surplus of
water comprises both surface run-off and groundwater storage.
94 2 Representation of Geographical Data Using Graphs
Procedures for Determining the Status of Water Availability
In an annual cycle of water balance estimation, the periods of soil moisture recharge
(R), water surplus (S), soil moisture utilization (U) and water deficiency (D) are
identified by the following procedures:
(a) In Table 2.18, month-wise water need and supply of a region for a theoretical
one-year period is shown, assuming the field capacity of the soil being 100mm.
In all themonths (January–May), the values of ‘Supplyminus need’ are positive
(supply of water is more than need) but from the month of June to September,
the negative values (need of water ismore than supply) indicate that morewater
will be withdrawn from underground than that will be recharged. Therefore,
June is the month from which the utilization of storage water starts. In the
‘Water budget section’ of Table 2.18, write ‘U’ for the utilization of water in
June.
(b) Utilization of water continues until the total of the negative values becomes
100 (field capacity of the soil is 100mm). If we add the values−53 and−88 for
the months of June and July, then the total value exceeds 100. It indicates that
July is the month of transition from water utilization to deficiency. Therefore,
in the ‘Water budget section’ write ‘U/D’ for the month of July (Table 2.18).
(c) In the ‘Water budget section’ write ‘D’ for all the months (in Table 2.18, for the
months of August and September) to indicate deficiency of water (the need for
water is more than supply) until the value becomes positive again. The positive
values (supply of water is more than the need) indicate the recharge of water
into the ground and it will be marked by the letter ‘R’ in the ‘Water budget
section’ (October and November in Table 2.18).
(d) Again, the recharge of water is converted to water surplus when the total of
the successive positive values exceeds 100 (field capacity of the soil). In the
month of December, the total of positive values exceeds 100 (9 + 82 + 91
= 182) indicating the time of transition from recharge to surplus of water.
Therefore, write ‘R/S’ in the ‘Water budget section’ for that month. Then all
the subsequent positive value is considered as the surplus of water and the letter
‘S’ is written in the ‘Water budget section’ (months of January–May in Table
2.18).
In this way, we will be able to easily determine the status of water availability of
any region for all the months in a year and rational decisions can be made on how
much and when water should be allocated for different purposes.
The surplus and deficiency of water of the sample study area during a normal
rainfall year are shown at monthly intervals in Table 2.19 and Fig. 2.29. Month-wise
rainfall (precipitation, P) and potential evapotranspiration (PE) have actually been
superimposed in Fig. 2.29. This figure reveals that from themonth of January toApril
amount of precipitation (P) exceeds potential evapotranspiration (PE), which is an
indicative of surplus ofwater during this period. Then the potential evapotranspiration
exceeds precipitation from the month of May to September. Consequently, the use
2.5 Types of Graphical Representation of Data 95
Table 2.19 Water budget estimation for a sample study area (elevation: 12 m; field capacity:
102 mm)
Month Jan Feb Mar Apr May June Jul Aug Sep Oct Nov Dec Total
P (mm) 148 123 103 67 55 50 35 35 61 119 152 170 1118
PE (mm) 13 21 29 39 58 76 89 82 70 50 24 14 565
P − PE +135 +102 +74 +28 −3 −26 −54 −47 −9 +69 +128 +156
�ST 0 0 0 0 −3 −26 −54 −19 0 +69 +33 0
ST (mm) 102 102 102 102 99 73 19 0 0 69 102 102
AE (mm) 13 21 29 39 58 76 89 54 61 50 24 14 528
D (mm) 0 0 0 0 0 0 0 28 9 0 0 0 37
S (mm) 135 102 74 28 0 0 0 0 0 0 95 156 590
of stored soil water was started and complete utilization of the stored water causes
a deficit of water from the middle of Augustto September. The perpendicular line
(R) drawn on the graph (Fig. 2.29) represents the complete utilization of stored soil
moisture. Again, precipitation exceeds potential evapotranspiration from the month
of October and continues up to April. A part of this water surplus compensates for
the loss of soil moisture or it triggers the recharge of water which is completed by
the middle of November. The perpendicular line (U) drawn on the graph (Fig. 2.29)
represents that the field capacity (102 mm) has been reached, i.e. the soil moisture
has been fully restored. The excess water obtained after saturation level of the field
capacity is attained and termed surplus of water (from the middle of November to
April) (Fig. 2.29).
Applicability of Water Balance Estimation
1. Water balance estimation is a useful method to assess the present status and
trends of the availability of water resources in a region for a particular period
of time.
2. Estimation of water balance assesses and improves the validity of visions,
scenarios and various strategies which strengthens the procedures of decision-
making for the proper management of water.
2.5.4.5 Hydrograph
A streamflow or discharge hydrograph at any point on a stream is a graph showing
the flow rate as a function of time at that point. In this graph, the discharge is plotted
on the y-axis (ordinate) and time is on the x-axis (abscissa) (Fig. 2.30). The units of
time may be in minutes, hours or days, and the rate of flow (discharge) is generally
expressed in cubic meters per second (cumec) or cubic feet per second (cusec).
Thus, the hydrograph is an important graphical representation of the topographic
96 2 Representation of Geographical Data Using Graphs
Fig. 2.29 Water balance curve of a sample study area
and climatic characteristics which control the inter-relationship between rainfall and
run-off of a particular drainage basin (Chow 1959). Though two types of hydrographs
are particularly important: the annual hydrograph and the storm hydrograph, but it is
more useful in hydrology to consider a hydrograph for a certain storm event (storm
hydrograph).
A storm hydrograph reflects the influence of all physical characteristics of the
river basin and, to some extent, also reflects the characteristics of the storm causing
the hydrograph. A hydrograph can be considered a thumbprint of a drainage basin.
The shape of a hydrograph mainly depends on the rate of transfer of water from
2.5 Types of Graphical Representation of Data 97
Fig. 2.30 Elements of a hydrograph
different parts of the river basin to the gauge station. No two river basins produce
the same hydrographs for the same storm. Hydrographs from similar river basins
may be similar, but not the same. In the same way, no two storms generate identical
hydrographs from the same basin.
Elements of the Hydrograph
The elements of the hydrograph are:
(1) Rising limb: As surface run-off reaches the gauge station, the water begins
to increase in the channel. With the progress of time, more and more surface
run-off reaches the gauge and the water in the channel continues to rise until
it reaches a maximum discharge, recorded as the maximum gauge height. The
rising portion of the hydrograph indicated by the rising stage is called the rising
limb (Fig. 2.30). The rising limb graphically represents increasing discharge
over time as the limb rises and discharge increases.
(2) Crest and peak discharge: The time interval of the greatest discharge at the
peak of the hydrograph is called the crest (Fig. 2.30). It may be of a short
time duration represented as a sharp peak or of a fairly long time duration
represented as a flat peak. The crest does not necessarily represent an equal
volume of discharges, rather it represents a zone having nearly equal highest
98 2 Representation of Geographical Data Using Graphs
discharges. The greatest discharge within the crest is called peak discharge
(Fig. 2.30) and it is of primary interest in hydrologic design.
(3) Recession or falling limb: The segment of the hydrograph after the peak is
called recession limb or falling limb (Fig. 2.30). It indicates the decrease of
discharge as water is withdrawn from the river basin storage after rainfall
ceases. The steepness of the recession limb represents the rate of draining of
water from the basin area.
(4) Point of inflection: The point on the recession limb indicating the end of storm
flow (i.e. quick flow or direct run-off) and the return to groundwater flow (i.e.
base flow) is known as the point of inflection (Fig. 2.30). In other words, it is
the point on the recession limb of the hydrograph where the steepness of the
slope of the graph starts to decline. It indicates the point where the base flow
becomes dominant to the total flow than the quick-response run-off.
(5) Time to peak: It is the time interval from the beginning of the rising limb
(beginning of the increase of discharge at the gauge station) to the peak
discharge (Fig. 2.30). It is largely controlled by the characteristics of the
drainage basin like travel distances, drainage density, channel slope, channel
roughness, soil infiltration capacity etc. The distributional pattern of rainfall
over the basin area is very important to alter the time to peak in a hydrograph.
For example, the hydrograph of a storm rainfall occurring on the upper part of
the basin area has a longer time to peak than for a storm rainfall occurring on
the lower basin area.
(6) Time of concentration: The time of concentration is the time needed for a
drop of water falling on the most distant part of the river basin to reach the
gauge station or the basin outlet (Fig. 2.30). It includes the time needed for all
parts of the river basin to contribute run-off to the hydrograph and this time
then indicates the highest discharge that can occur from certain storm intensity
over the river basin area.
(7) Lag time: Lag time is the time distance between the centre of mass of effective
rainfall and the centre of mass of the direct run-off hydrograph. As the deter-
mination of the centre of mass of the direct run-off hydrograph is difficult, lag
time is also defined as the time distance between the centre of mass of effective
rainfall and the peak of the direct run-off hydrograph (Fig. 2.30). It assumes
uniform effective rainfall over the entire basin area.
Factors Affecting Hydrograph Characteristics
Several factors affect the characteristics of a stream hydrograph. These include:
(1) Drainage characteristics: The characteristics of the drainage are primarily
derived from the parent geology of the drainage basin and affect the charac-
teristics of the streamflow as well as the hydrograph. Large drainage basins
receive more precipitation (rainfall) than the smaller basin, so have a greater
peak discharge in comparison to smaller basins. Generally, smaller basins have
shorter lag times than the larger basins because rainwater does not have to
2.5 Types of Graphical Representation of Data 99
travel long distances. Circular basins lead to shorter lag times and a greater
peak discharge than elongated basins because the water in the former has a
shorter distance to travel to reach a river. River basins with a steep slope are
likely to have a shorter lag time than the basins with a gentle slope because
the water in the former flows more quickly down to the river. Basins with high
drainage density drain more quickly, so have a smaller lag time. In a saturated
river basin, the surface run-off increases and rainwater comes into the river
more quickly which reduces the lag time. If the drainage basin is dominated
by impermeable rock, infiltration will be reduced and surface run-off will be
higher which increases the peak discharge and reduces the lag time.
(2) Type and distribution of precipitation: The precipitation in the form of snow
is likely to have a greater lag time rather than rainfall because snow takes time
to be melted before the water reaches the river channel. Amount of rainfallis very important to control the nature of the storm hydrograph. Heavy storm
rainfall results in more supply of water in the drainage basin leading to a higher
discharge of water.
(3) Soil and Land use: Soil type and land use pattern may alter the characteris-
tics of the hydrograph. Forest removal, grass cutting, urbanization, farming,
building of roads and any other structures reduce the rate of infiltration and
increases the run-off. The presence of more vegetation in the basin area inter-
cepts precipitation (rainfall) and slows the draining of water into river channels
and so the lag time increases.
(4) Human factors: Rapid rate of urbanization by the human being increases
the concentration of impermeable materials on the surface which reduces the
infiltration level and surface run-off increases. This results in an increase in
peak discharge and a shorter lag time.
Delineation of Run-Off Components in Storm Hydrograph
A streamflow hydrograph of a specific storm is a hydrograph of total run-off. Compo-
nents of streamflow are (a) direct run-off and (b) base flow. Direct run-off is again
divided into surface run-off and quick interflow, whereas the base flow is also divided
into delayed interflow and groundwater run-off.
Surface Run-Off
Surface run-off is that portion of the run-off water that travels over the ground
surface to the stream channel (Fig. 2.31a). Most surface run-off flows to the first-
order channels because they collectively drain the largest area of the drainage basin.
Surface run-off includes that portion of the precipitation directly falling on the water
flowing in the channel but overland flowdoes not include this portion of precipitation.
100 2 Representation of Geographical Data Using Graphs
Fig. 2.31 Various components of run-off (after Singh 1994)
Interflow or Sub-surface Flow
It is the surface water that infiltrates the surface layer and moves laterally beneath
the surface to a channel (Fig. 2.31c). Interflow can occur on forest floors, where the
needles, leaves and other debris of the plants cover the ground surface. In interflow,
the water is subject to higher flow resistance than the surface run-off. Because of
this, the interflow water does not move as faster as surface run-off, hence delayed in
reaching the stream channel.
Direct Run-Off
Direct run-off is considered to be the sum of surface run-off and the interflow. It
is frequently equated with surface run-off. These two flow components move faster
than groundwater flow and hence are often lumped together for hydrologic processes.
Base Flow
Base flow or groundwater flow is that component of the flow that contributed to the
stream channel through groundwater (Fig. 2.31d). Groundwater occurs from surface
water infiltration to the water table and then moving laterally to the stream channel
through the aquifer. Such water moves very slowly than direct run-off and because of
this reason it does not contribute to the peak discharge for a given storm hydrograph.
Important components of streamflow can be easily separated and illustrated in a
storm hydrograph. In Fig. 2.32, point ‘A’ marks the initiation of the surface run-off,
which is believed to end at the change in slope shown as ‘B’; point ‘B’ is considered
to be the initiation of interflow, which ends at point ‘C’; point ‘C’ marks the initiation
of groundwater flow, which continues up to the end of the hydrograph. Therefore, the
segment of the curve from A to B indicates the contribution of surface run-off, B to
C indicates the contribution of interflow, especially the quick interflow and beyond
‘C’ it indicates the contribution of delayed interflow or base flow or groundwater
flow.
2.5 Types of Graphical Representation of Data 101
Fig. 2.32 Important components of streamflow hydrograph
2.5.4.6 Rating Curve
Rating curve (also called stage–discharge relation curve) is the graphical represen-
tation of the relationship between stream stage and stream flow or discharge of water
(cusec or cumec) (Fig. 2.33 and Table 2.20) for a given point on a stream, generally at
gauging stations. In rating curve, measured discharge is usually plotted on the x-axis
(abscissa) and measured stage on the y-axis (ordinate) (Fig. 2.33). Stream stage (also
called gauge height or stage) means the height of the water surface (in feet) above
a well-known elevation where the stage is zero. Though the zero stage is arbitrary,
Fig. 2.33 Rating curve (Relationship between stream stage and discharge)
102 2 Representation of Geographical Data Using Graphs
Table 2.20 Stream stage and discharge relationship
Sl. no Gauge height (ft) Discharge (cubic
ft/s)
Sl. no Gauge height (ft) Discharge (cubic
ft/s)
1 0.5 16 19 6.1 150
2 0.65 26 20 6.8 162
3 1.0 30 21 7.25 163
4 1.15 37 22 7.6 210
5 1.5 35 23 8.6 220
6 2.0 38 24 8.5 230
7 2.2 51 25 9.3 269
8 2.6 52 26 9.6 315
9 3.1 78 27 9.5 296
10 3.25 62 28 9.75 310
11 3.85 78 29 10.4 340
12 4.1 95 30 10.6 371
13 4.5 96 31 10.7 367
14 4.65 104 32 10.75 384
15 4.9 120 33 10.9 401
16 5.0 103 34 10.95 406
17 5.6 122 35 11.1 430
18 5.8 132 36 11.2 407
generally it is close to the streambed. Stream discharge is measured several times
over a range of stream stages. These measurements are done over a period of months
or years for the establishment of an accurate relationship between the discharge and
gauge height at the gauging station. Additionally, these relationships must constantly
be verified against ongoing stream flow or discharge measurements because stream
channels are always changing.
Controls of Rating Curve
Rating curve represents the integrated result of a wide variety of channel and flow
parameters. The combined effect of these parameters is considered as control. If the
rating curve (stage–discharge relationship) remains the same with time, then it is
called permanent control. But if the relationship does change with time, it is called
shifting control. When the control of a gauging station changes, the rating curve also
changes. The changemay be caused by (1) erosion or deposition, (2) rapidly changing
flow, (3) varying backwater, and (4) changes in the flow because of dredging, channel
encroachment and weed growth. For the shifting control due to cases (1) and (4),
frequent current meter gauging is required (Singh 1994). Bedrock-bottomed parts
of streams or metal/concrete structures or weirs are generally, though not always,
thought of as permanent controls.
2.5 Types of Graphical Representation of Data 103
Steps of Development of Rating Curve
The development of rating curve generally involves three steps:
1. Measuring stream stage
A continuous record of the stream stage, i.e. the height of the water surface at a
specific location along a stream is taken.
Various methods are used tomeasure the stream stage or gauge height. A common
method is with a stilling well in the river bank or fixed to a bridge pier.Water from the
stream comes into and leaves the stilling well through the underwater pipes which
allow the water surface in the stilling well to be at the same height as the water
surface in the stream. The height of the water surface inside the stilling well can
be easily measured using pressure or float optic or acoustic sensor. The measured
stream stage values are stored in an electronic data recorder device at a regular time
interval, generally every 15 min interval.
A stilling well is not cost-effective to install; stream stage can also be determined
by the measurement of the pressure needed to maintain a little flow of gas through a
tube and bubbled out at a specified location below water in the stream. The pressure
is directly linked to the height of the water column over the tube outlet in the stream.
More the height of water above the tube outlet, more pressure is needed to push the
gas bubbles through the tube.
2. The discharge measurement
Discharge of water (the volume of water passing a specific location along a stream
per unit of time) is measured periodically. Generally, streamdischarge is estimated
by multiplying the area of stream cross-section by the average water velocity in that
cross-section:
Discharge of water = area of the cross − sect i on
× average water veloci t y (2.16)
Numerousmethods and types of equipment are used tomeasure the water velocity
and cross-sectional area, including the water current meter and acoustic Doppler
current profiler.
The current meter is used to measure the velocity of water at prefixed places (sub-
sections) along a specified line, like a bridge or suspended cableway across a stream
or river. In this technique, the stream cross-section is divided into several numbers
of vertical sub-sections. The area of each sub-section is obtained by multiplying its
width and depth, and the water velocity is measured using the current meter. Then the
discharge of water in each sub-section is computed by multiplying the sub-section
area and the measured water velocity. The total discharge in a cross-section is then
calculated by summing the discharge of each sub-section.
Acoustic Doppler current profiler (ADCP) can also be used to measure the water
discharge. An ADCP uses the Doppler effect to measure the water velocity. ADCP
transmits a sound pulse into the stream water and detects the shift in the frequency
104 2 Representation of Geographical Data Using Graphs
of that pulse reflected back to the receiver of ADCP by sediment or other particulate
matters transported in the water. The change in frequency or Doppler shift, which is
detected by the ADCP, is then converted into water velocity. The discharge of water
is then calculated by multiplying the cross-section area with the measured water
velocity.
3. The stage–discharge relation
Identification of the natural and continuously changing relationship between the
stream stage and discharge can be done by applying the stage–discharge relation to
transform the frequently measured stream stage into estimates of discharge (USGS
Science for a changing world).
Simple Rating Curve
The representation of measured values of stream stage and water discharge on an
arithmetic scale results in a parabolic curve, which can be expressed as
Q = a(h − b)c (2.17)
where b is a constant indicating the gauge reading for zero discharge, a and c are
rating curve constants. When the measured stream stage and water discharge data are
represented on a logarithmic scale, a straight line results and the Eq. (2.17) becomes
log Q = log a + c log(h − b) (2.18)
The values of constants a and c can be obtained using the least squaremethod. The
value of constant b must be calculated beforehand and this can be done in different
ways. A trial-and-error method can be used to get the value of b, which then gives the
best-fit curve. Another way is to extrapolate the rating curve corresponding to Q = 0
and then plot log Q versus log(h − b). If the plotting of the values gives a straight line
then the value of b obtained by extrapolation is correct and acceptable. Otherwise,
another value in the vicinity of the previous value of b is chosen and the same
procedure is repeated (Singh 1994). The value of b can also be computed analytically.
From a smooth curve of Q versus h, the values of discharge like Q1, Q2 and Q3
are selected in such a way that Q1
Q2
= Q2
Q3
. The corresponding values of the stage are
h1, h2 and h3. Then we have
(h1 − b)c
(h2 − b)c
= (h2 − b)c
(h3 − b)c
(2.19)
or
h1 − b
h2 − b
= h2 − b
h3 − b
(2.20)
2.5 Types of Graphical Representation of Data 105
from which the value of b is derived as
b = h1h3 − h2
2
h1 + h3 − 2h2
(2.21)
Alternatively, the values of these parameters a, b and c can be obtained by
optimization.
Generally, simple rating curve is satisfactory formost of the streams inwhich rapid
fluctuations of stream stage are not experienced at the gauging section. The adequacy
of the curve ismeasured by the scattering of values around the fitted curve. If there is a
permanent control, the rating curve is basically permanent. In some gauging stations,
theremay be two ormore controls each for a specific range of stream stage. The rating
curve in such a station is discontinuous; the point of discontinuity corresponds to the
stream stage revealing the change in control. An example is when submergence of a
weir control starts when the tailwater level below the control rises above the lowest
point of the control. Even in such situations, the simple rating curve may well be
acceptable if the control is permanent, free of backwater and the slope of the streams
is steep.
Uses of Rating Curve
Continuous measurement of stream gauges provide streamflow/discharge informa-
tion which can be used for different purposes including.
(i) Flood prediction
(ii) Water management and allocation
(iii) Engineering design
(iv) Research purposes
(v) Operation of locks and dams
(vi) Recreational safety and enjoyment etc.
2.5.4.7 Lorenz Curve and Gini Coefficient
The concentration or inequality in the distribution of any phenomenon or attribute
or variable with respect to others can be studied in several different methods like (1)
Lorenz curve and Gini coefficient, (2) location quotient and (3) index of dissimilarity
(Mahmood 1999). The Lorenz curve is the graphical method and the Gini coefficient
is the numerical or mathematical method of measurement of the degree of inequality
of different phenomena or variables.
Lorenz curve (or Pareto curve), a form of percentage cumulative frequency curve,
was first developed in 1905 by Max Otto Lorenz, an American economist for repre-
senting the inequality in the distribution of wealth or income. It is an effective graph-
ical measure of inequality in the distribution of various items in social science,
especially in geography, like studies on landholdings, income, expenditure, wealth,
106 2 Representation of Geographical Data Using Graphs
economic activities etc. (Pal 1998). It basically deals with the cumulative percentage
distributions of the two attributes or variables at different points. For example, for
the representation of income of the people in a country, this curve appears as a graph
of population shares against their income shares, ordered from poorest to richest.
Techniques of Drawing of Lorenz Curve
(1) At first, both the variables are expressed in percentages (%), arranged according
to ascending or descending order and their cumulative percentages are calcu-
lated (Tables 2.21, 2.22 and 2.23). Cumulative percentages of one variable
(independent) are plotted on the x-axis and cumulative percentages of other
variable (dependent) are plotted on the y-axis. For example, in the study of the
number and area of landholdings, the cumulative percentage of the number of
land holdings is plotted on the x-axis and the cumulative percentage of the area
of landholdings is plotted on the y-axis (Fig. 2.34). Similarly, in the study of
income distribution of the people, the cumulative percentage of population is
plotted on the x-axis and the cumulative percentage of income is plotted on the
y-axis (Fig. 2.36).
(2) Cumulative percentages of one variable up to certain points are plotted on a
graph against the cumulative percentages of the other variable up to the same
points. The different points so obtained are then joined by a smooth freehand
curve, known as Lorenz curve.
(3) For comparison, a diagonal line at an angle of 45° is also drawn, joining the
point of origin or lower-left corner (x = 0% and y = 0%) and the last point or
upper-right corner (x = 100% and y = 100%) of the graph. This line is called
‘line of equal distribution’ (Figs. 2.34, 2.35 and 2.36). Lorenz curve will never
cross the line of equal distribution.
How to Read the Lorenz Curve
(1) If 1% share of ‘x’ variable corresponds to 1% share of ‘y’ variable, 50% share
of ‘x’ variable corresponds to 50% share of ‘y’ variable and n% share of ‘x’
variable corresponds to n% share of ‘y’ variable, then this is the condition of
equal distribution of two variables. Thus the Lorenz curve in the idealcase
would be a straight line (equal distribution line).
For example, if we want to understand the degree of inequality in the distribution
of income of the people in a region or country and if 1% of the population has 1%
of the total income, 50% of the population has 50% of the total income and n%
population has n% of the total income, then the distribution of income among the
people is perfectly equal.
(2) The deviation of any Lorenz curve from the equal distribution line is in propor-
tion to the degree of inequality in the distribution of one variable in relation to
2.5 Types of Graphical Representation of Data 107
Ta
bl
e
2.
21
W
or
ks
he
et
fo
r
L
or
en
z
cu
rv
e
(T
he
nu
m
be
r
an
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la
nd
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ld
in
gs
)
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ze
of
la
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in
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(h
ec
ta
re
s)
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o.
of
la
nd
ho
ld
in
gs
(i
n
m
ill
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ns
)
A
re
a
of
la
nd
ho
ld
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gs
(i
n
m
ill
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ct
ar
es
)
%
of
no
.o
f
la
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ld
in
gs
to
to
ta
l
no
.o
f
la
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ld
in
gs
%
of
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la
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to
to
ta
l
ar
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of
la
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C
um
ul
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%
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no
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to
to
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no
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(X
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C
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%
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la
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l
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108 2 Representation of Geographical Data Using Graphs
Ta
bl
e
2.
22
W
or
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he
et
fo
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L
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cu
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To
ta
lp
op
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(T
P)
U
rb
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la
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(U
P)
%
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P
to
T
P
%
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T
P
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ra
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T
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(1
)
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To
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(2
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C
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So
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C
en
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of
In
di
a
(2
01
1)
2.5 Types of Graphical Representation of Data 109
Table 2.23 Inequality in the distribution of income of people of Sweden, USA and India
Decile % Income of people Cumulative % income of people
Sweden USA India Sweden USA India
1 3.3 1.9 0.6 3.3 1.9 0.6
2 6.2 3.8 1.2 9.5 5.7 1.8
3 7.4 5.5 3.0 16.9 11.2 4.8
4 8.4 6.8 5.1 25.3 18.0 9.9
5 9.3 8.2 6.2 34.6 26.2 16.1
6 10.2 9.5 6.9 44.8 35.7 23
7 11.1 11.2 7.2 55.9 46.9 30.2
8 12.3 13.3 9.4 68.2 60.2 39.6
9 13.7 16.1 25.4 81.9 76.3 65.0
10 18.1 23.7 35.0 100 100 100
Sources Statistics Sweden, online database (2014), U.S. Census Bureau, Historical Income Tables
(2016); Credit Suisse’s Global Wealth Databook (2014)
Fig. 2.34 Lorenz curve showing the inequality in the distribution of number and area of land
holdings
110 2 Representation of Geographical Data Using Graphs
Fig. 2.35 Lorenz curve showing the inequality in the distribution of total and urban population
the other. Further, this Lorenz curve is from the line of equal distribution, so
greater is the inequality. If the Lorenz curve coincides with the line of equal
distribution, it indicates ‘0’ inequality. But, if the curve coincides with ‘x’ and
‘y’ axes then it indicates the maximum (unity or 100%) inequality.
Gini Coefficient (G)
The inequality in the distribution of any phenomenon is numerically measured by
an index known as ‘Gini coefficient’, developed by the Italian statistician Corrado
Gini in the year 1912. Gini coefficient is the ratio of the area under the Lorenz curve
and the equal distribution line to the area of the triangle formed by the x-axis, y-
axis and the equal distribution line. Graphically, the Gini coefficient is defined as a
ratio of two areas occupying the summation of all vertical differences between the
Lorenz curve and the equal distribution line (‘A’ in Figs. 2.34 and 2.35) divided by
the difference between the perfect equal distribution line and perfect inequality lines
(‘A + B’ in Figs. 2.34 and 2.35). Therefore, the Gini coefficient can be defined as
A
A+B (shown in Figs. 2.34 and 2.35). In the case of uniform distribution, the Lorenz
curve will fall on the line of equal distribution. Then the area between the curve and
the line of equality would be zero (A = 0) and the value of Gini coefficient becomes
0 which means perfect equality. For the distribution with maximum concentration or
2.5 Types of Graphical Representation of Data 111
Fig. 2.36 Lorenz curve showing the inequality of income distribution of people in Sweden, USA
and India SourcesStatistics Sweden, online database (2014), U.S. CensusBureau,Historical Income
Tables (2016); Credit Suisse’s Global Wealth Databook (2014).
inequality, the curve will coincide with ‘x’ and ‘y’ axes. Then the area of ‘B’ would
be 0 (B = 0), i.e. the area between the Lorenz curve and the equal distribution line
becomes equal to the area of the triangle formed by the x-axis, y-axis and the equal
distribution line and the value of Gini coefficient becomes unity or 1, which means
perfect inequality. Thus the value of Gini coefficient varies on a scale between zero
(0) and unity (1 or 100%) [0 ≤ G ≤ 1].
The value ofGini coefficient (G) can be numerically calculated using the following
formula:
G = 1
100 × 100
∣∣∣
∑
(Xi.Yi+1) −
∑
(Yi.Xi+1)
∣∣∣ (2.22)
where Xi and Yi are the cumulative percentage distributions of the two attributes.
For the data shown in Table 2.21,
G = 1
100 × 100
|36693.37 − 32106.65|
G = 1
10000
|4586.72|
112 2 Representation of Geographical Data Using Graphs
G = 4586.72
10000
G = 0.4586
G = 0.46 (Round off)
The value of Gini coefficient (G) can also be worked out graphically using the
following technique:
In Fig. 2.34, the length of the straight line ‘xr’ is 5.9 cmand this length is equivalent
to the inequality of unity (1). The line ‘xr’ cuts the Lorenz curve at the point ‘p’ and
the distance ‘pr’ is 2.7 cm. Hence, the degree of inequality (G) can be calculated as
pr
xr = 2.7 cm
5.9 cm , i.e. G = 0.4576 = 0.46 (Round off).
Uses of the Lorenz Curve and Gini Coefficient
• Lorenz curve is the simplest representation and the Gini coefficient is the easiest
measurement of inequality and can be interpreted easily.
• It is the most effective measure in comparing the differences between two and
more data distributions.
• It can be easily applied to understand the change of distribution of any
phenomenon within a country or region over a period of time, i.e. whether the
inequality in the distribution is increasing or decreasing.
• It displays the distribution of wealth or income of a country or region among the
population withthe help of a graph.
• It can be effectively used while introducing specificmeasures for the development
of the weaker sections in the economy.
• It can be applied to explain the fruitfulness of a government policy implemented
to help the redistribution of income.
Problems of Using Lorenz Curve and Gini Coefficient
• Data restrictions, i.e. negative values cannot be represented.
• It might not always rigorously be accurate for a finite population.
• When two Lorenz curves intersect, it is difficult to ascertain which distribution
illustrated by the curves represents more inequality.
• Gini coefficient as a measure of index of concentration should not be compared
with the degree of concentration of a phenomenon or activity in a region to which
the ‘location quotient’ is concerned with.
• Decision-makers and researchers are most interested in analysing inequality by a
number.
For the data given in Table 2.22,
2.5 Types of Graphical Representation of Data 113
G = 1
100 × 100
|18281.15 − 15745.24|
G = 1
10000
|2535.91|
G = 2535.91
10000
G = 0.2536
G = 0.25 (Round off)
In Fig. 2.35, the length of the straight line ‘xr’ is 5.6 cmand this length is equivalent
to the inequality of unity (1). The line ‘xr’ cuts the Lorenz curve at the point ‘p’ and
the distance ‘pr’ is 1.4 cm. Hence, the degree of inequality (G) can be calculated as
pr
xr = 1.4 cm
5.6 cm , or G = 0.25.
(a) Inequality in the distribution of income of population in Sweden
In Fig. 2.36, the length of the straight line ‘px’ is 6.0 cm and this length is equivalent
to the inequality of unity (1). The line ‘px’ cuts the Lorenz curve of Sweden at the
point ‘q’ and the distance ‘pq’ is 1.0 cm.
Hence, the degree of inequality (G) can be calculated as pq
px = 1.0 cm
6.0 cm = 0.17.
(b) Inequality in the distribution of income of population in the USA
The line ‘px’ cuts the Lorenz curve of USA at the point ‘r’ and the distance ‘pr’ is
1.5 cm.
Hence, the degree of inequality (G) can be calculated as pr
px = 1.5 cm
6.0 cm = 0.25.
(c) Inequality in the distribution of income of population in India
The line ‘px’ cuts the Lorenz curve of India at the point ‘s’ and the distance ‘ps’ is
2.5 cm.
Hence, the degree of inequality (G) can be calculated as ps
px = 2.5 cm
6.0 cm = 0.42.
Therefore, it is clear that the distribution of income of the people is more unequal
in India (G = 0.42) compared to Sweden (G = 0.17) and the USA (G = 0.25).
In India, the bottom 10% of the people possess only 0.6% of the total income of
the country whereas it is 3.3% and 1.9% of total national income in the case of
Sweden and the USA, respectively. The richest 10% of people in India enjoy 35%
of the country’s national income which is almost double the income of the top 10%
of people in Sweden (18.1%). In the USA, the top 10% of people have 23.7% of
the total national income. In India, 50% of the people have only 16.1% of the total
income of the country whereas it is 34.6% and 26.2% of total national income in the
case of Sweden and the USA, respectively.
114 2 Representation of Geographical Data Using Graphs
2.5.4.8 Dispersion Graph
It is observed that in any set of data the actual values differ from each other and from
the mean or average value also. The measurement and analysis of this spread-out
character of the data set is called ‘dispersion’. In other words, dispersion indicates
the degree of heterogeneity among the values in a data set. More the heterogeneity
among the values, the more the degree of dispersion. Dispersion is as characteristic
as the similarity is in statistics. It can be measured using two methods: (1) by means
of the distances between specific observed values and (2) by means of the average
deviations of individual observed values about the central value (Pal 1998).
When dispersion is measured in terms of the difference between the highest and
the lowest values of the observations in a data set then it is called ‘range’. It is used
when the values in a data set form distance between points and individuals and when
it is arranged graphically in terms of their magnitude, then a ‘dispersion graph’ is
obtained. The total spread of the data within the range can be obtained from this
graph. Symbolically speaking,
Coefficient of range = L − S
L + S
(2.23)
where L and S are the largest and smallest values, respectively.
Dispersion graphs are normally used to show the most important pattern in the
distribution of the data set. The graph displays each value plotted as an individual
point on a vertical scale. It shows the range of data and the distribution of each
individual value within that range. Rainfall dispersion graph is one in which each
year seasonal and annual amounts of rainfall are represented by placing a point
against a vertical scale to enable to observe at a glance the span of dry years, normal
years and wet years over a period of time.
Methods of Construction of Rainfall Dispersion Graph
• At first the fundamental values like median (Q2), upper quartile (Q3) and lower
quartile (Q1) etc. of the given data set are obtained using suitable formula.
• To obtain these values all the observations are arranged into ascending order. To
obtain the value of the lower quartile (25% observations are smaller and 75%
observations are larger than this value), consideration should be taken from the
lower end and in the case of the upper quartile (75% observations are smaller and
25% observations are larger than this value) consideration should be taken from
the upper end of the data set. In our given example with annual rainfall data for
30 years, the lower quartile (Q1) will lie at the 7.75th position of the series, and
the upper quartile (Q3) will lie at 23.25th position (Table 2.24). The 15.5th value
reckoned from the bottom or top of the graph indicates the median or Q2 which
divides the entire data set into two equal halves (Fig. 2.37).
2.5 Types of Graphical Representation of Data 115
Table 2.24 Calculations for rainfall dispersion graph (Annual rainfall of Bankura district, year
1976–2015)
Rainfall in ascending order Position Rainfall in ascending order Position
1040 1 1620 16
1062 2 1645 17
1092 3 1678 18
1092 4 1690 19
1129 5 1765 20
1156 6 1780 21
1280 7 1828 22
1288 8 1856 23
1290 9 1856 24
1290 10 1876 25
1452 11 1959 26
1467 12 1975 27
1560 13 1993 28
1569 14 2014 29
1595 15 2128 30
Lower quartile (Q1) 1286 mm (7.75th position)
Median (Q2) 1607.5 mm (15.5th position)
Upper quartile (Q3) 1856 mm (23.25th position)
Co-efficient of Quartile Deviation 0.1814
• A suitable vertical scale is selected and then each value of the data set (annual
rainfall) are plotted graphically as individual points for the whole of the period
under consideration on that vertical scale (Fig. 2.37).
• The central value (the median value, Q2) is selected and this is displayed on
the graph. Similarly the values of Q1 and Q3 are also displayed on the graph to
understand the dispersion or variability among the observations within the graph.
Figure 2.37 illustrates the 30 years of annual rainfall distribution of Bankura
district in a dispersion graph.
Advantages
• Easy to understand visually.
• Represents the spread of data from the mean and conveys much more information
than other graphs drawn on mean values alone.
• Can find out the values of range, mean, median, mode, lower quartile, upper
quartile and inter-quartile range.
• Can show the anomalies in the data set.
• It makes it possible to compare the variability of two or more sets of data.
116 2 Representation of Geographical Data Using Graphs
Fig. 2.37 Rainfall
dispersion graph of Bankura
district (year 1976–2015)
Disadvantages
• Better to work with lots of data.
• Sometimes the important features of the rainfall distribution may not be shown.
2.5 Types of Graphical Representation of Data 117
2.5.4.9 Rank-Size Graph
The rank-size-rule or rank-size relationship is an empirical and practical regularity
of city size distribution observed in theurban systems inmany countries in the world.
It is an important method for analysing the total settlement networks in a region or
country. Hence, it is a technique for understanding the national settlement system and
facilitate the depiction and interpretation of the relationship between the population
size and rank of the urban places. The rank-size-rule was first identified by Auerbach
in 1913 but postulated and popularized by G.K. Zipf in 1949 in his book ‘Human
behaviour and the principle of least effort’.After that,manygeographers have studied
the size distribution of settlements and described the relationship between the number
and size of the settlements in geographical form.
In its general form, the rule states that, if all urban areas or cities in a country
or region are ranked according to the population size with the largest city having
the first rank, then the population of any urban area or city multiplied by its rank
will equal the population of the first ranking city (largest city). In other words, the
population of a city or urban area (Pr ) of rank r can be calculated by dividing the
population of the first ranking city (P1) by its rank.
Symbolically, it can be written as
Pr = P1
r
(2.24)
where Pr is the population of ‘r’ ranking city; P1 is the population of the first ranking
city and r is the rank of the city.
Accordingly, the second-ranking city of a country or region has half of the popu-
lation of the largest city; the third-ranking city has one-third of the population of the
largest city and so on down the scale (Table 2.25).
The relationship can be represented graphically by plotting the population of the
city with respect to its rank. If rank (on ‘x’-axis) and population (on ‘y’-axis) are
plotted using arithmetic scale then a curve (inverted J-shape) results (Fig. 2.38). But
plotting of the population against the rank following logarithmic scale will produce
a straight line (Fig. 2.39). When logarithmic scales are considered along both the
axes then the equation can be rewritten as
log Pr = log
(
P1
r
)
(2.25)
log Pr = log P1 − log r (2.26)
Rank-Size Graph According to Zipf (1949)
118 2 Representation of Geographical Data Using Graphs
Fig. 2.38 Rank-size graph according to G.K. Zipf (arithmetic scale)
Fig. 2.39 Rank-size graph according to Pareto (logarithmic scale)
2.5 Types of Graphical Representation of Data 119
G.K. Zipf used the method, shown in Table 2.25 to compute the expected
population of different cities or urban areas in a country or region.
Rank-Size Graph According to Pareto
According to this rule, the relation between the population of a town or city and its
rank can be expressed as follows (Pareto’s distribution):
Pr = K · r−b (2.27)
where Pr is the population of the ‘r’ ranking city. K and b are the constants.
The above equation gets transformed into the following linear form after taking
the logarithm on both sides:
log Pr = log(K · r−b) (2.28)
log Pr = log K − b log r (2.29)
Table 2.25 Rank-size relationship of Indian cities (according to G.K. Zipf method)
City Total (actual) population
(2011 census)
Rank (r) 1
rank (r)
Expected or estimated
total population
[∑
Total population
∑ 1
r
]
× 1
r
Mumbai 18,394,912 1 1 31,898,746
Delhi 16,349,831 2 0.5 15,949,373
Kolkata 14,035,959 3 0.33 10,526,586
Chennai 8,653,521 4 0.25 7,974,687
Bangalore 8,520,435 5 0.20 6,379,749
Hyderabad 7,674,689 6 0.17 5,422,787
Ahmedabad 6,361,084 7 0.14 4,465,824
Pune 5,057,709 8 0.125 3,987,343
Surat 4,591,246 9 0.11 3,508,862
Jaipur 3,046,163 10 0.10 3,189,875
Kanpur 2,920,496 11 0.09 2,870,887
Lucknow 2,902,920 12 0.08 2,551,900
Nagpur 2,497,870 13 0.077 2,456,203
Ghaziabad 2,375,820 14 0.07 2,232,912
Indore 2,170,295 15 0.067 2,137,216
Total 105,552,950
∑ 1
rank = 3.309
120 2 Representation of Geographical Data Using Graphs
This equation can be equated with the regression equation:
Y = a − bX (2.30)
where Y = log Pr ; X = log r ; a = log K .
b =
∑
XY −
∑
X
∑
Y
n
∑
X2 − (
∑
X)2
n
(2.31)
b = 80.1987 − 12.11649×101.0695
15
11.40195 − (12.11649)2
15
b = 80.1987 − 1224.607586055
15
11.40195 − 146.8093299201
15
b = 80.1987 − 81.640505737
11.40195 − 9.78728866134
b = −1.441805737
1.61466133866
b = −0.8929462188
a = Y − bX (2.32)
a = 101.0695
15
− (−0.8929462188)
12.11649
15
a = 6.73796666667 − (−0.8929462188) × 0.807766
a = 6.73796666667 + 0.72129159538
a = 7.45925826205
Thus, log Pr = 7.45925826205 − 0.8929462188 log r .
Here, a = log K = 7.45925826205 and b = 0.8929462188.
So, log K = 7.45925826205.
where K = Antilog of 7.45925826205.
Hence, K = 28,791,100.
So, the original equation (Eq. 2.27) can be written in the following form:
Pr = 28791100.r−0.8929462188 (2.33)
2.5 Types of Graphical Representation of Data 121
Table 2.26 Rank-size relationship of Indian cities (according to Pareto method)
City Total (actual)
population
(Pr )
Rank (r) X = log r X2 Y = log Pr XY
Mumbai 18,394,912 1 0 0 7.2646977 0
Delhi 16,349,831 2 0.301029 0.090618 7.2135132 2.1714476
Kolkata 14,035,959 3 0.477121 0.227644 7.1472420 3.4100992
Chennai 8,653,521 4 0.602059 0.362475 6.9371928 4.1765993
Bangalore 8,520,435 5 0.698970 0.488559 6.9304617 4.8441848
Hyderabad 7,674,689 6 0.778151 0.605518 6.8850607 5.3576168
Ahmedabad 6,361,084 7 0.845098 0.714190 6.8035311 5.7496505
Pune 5,057,709 8 0.903089 0.815569 6.7039538 6.0542669
Surat 4,591,246 9 0.954242 0.910577 6.6619305 6.3570938
Jaipur 3,046,163 10 1 1 6.4837531 6.4837531
Kanpur 2,920,496 11 1.041392 1.084497 6.4654566 6.7330747
Lucknow 2,902,920 12 1.079181 1.164631 6.4628350 6.9745687
Nagpur 2,497,870 13 1.113943 1.240869 6.3975698 7.1265280
Ghaziabad 2,375,820 14 1.146128 1.313609 6.3758135 7.3074983
Indore 2,170,295 15 1.176091 1.383190 6.3365187 7.4523226
Total
∑
Pr =
10,55,52,950
∑
r =
120
∑
X =
12.11649
∑
X2 =
11.40195
∑
Y =
101.0695
∑
XY =
80.1987
As per the rank-size relationship, by substituting ‘r’= 1, 2, 3, 4 etc. in Eq. (2.33),
we get the estimated population of cities ranking 1st, 2nd, 3rd, 4th etc. The population
of the top 15 cities in India are estimated based on the fitted rank-size relationship in
the given Eq. (2.33) and the results are given in Tables 2.26 and 2.27. The graphical
representation of the result is shown in Fig. 2.39.
It must be noted that the differences between actual and estimated populations
(shown in Table 2.27) have been calculated based on the relationship between 15
cities only. These differences may be reduced if more numbers of cities are taken
into consideration in determining the relationship.
Types of Deviations in Rank-Size Rule
Three main types of deviations in the rank-size rule are as follows (Siddhartha and
Mukherjee 2002):
Primary Deviation
The population of the second-largest city is less than half the population of the
largest city, i.e. a condition for the development of primate city (the city having
122 2 Representation of Geographical Data Using Graphs
Table 2.27 Expected populations and their deviations from actual populations
City Rank (r) Actual
population
Estimated
population
Difference % Difference
Mumbai 1 18,394,912 28,791,100 1,03,96,188 36.11
Delhi 2 16,349,831 15,504,389 −845,442 −5.45
Kolkata 3 14,035,959 10,794,800 −3,241,159 −30.02
Chennai 4 8,653,521 8,349,319 −304,202 −3.64
Bangalore 5 8,520,435 6,840,937 −1,679,498 −24.55
Hyderabad 6 7,674,689 5,813,143 −1,861,546 −32.02
Ahmedabad 7 6,361,084 5,065,603 −1,295,481 −25.57
Pune 8 5,057,709 4,496,219 −561,490 −12.49
Surat 9 4,591,246 4,047,352 −543,894 −13.44
Jaipur 10 3,046,163 3,683,935 637,772 17.31
Kanpur 11 2,920,496 3,383,378 462,882 13.68
Lucknow 12 2,902,920 3,130,454 227,534 7.27
Nagpur 13 2,497,870 2,914,518 416,648 14.29
Ghaziabad 14 2,375,820 2,727,894 352,074 12.91
Indore 15 2,170,295 2,564,909 394,614 15.38
Total
∑
r = 120
∑
Pr =
10,55,52,950
108,107,950 25,55,000 −30.23
twice or more population than the next ranking city in the urban hierarchy) emerges
(Fig. 2.40). Aprimate city is developed when few simple strong forces operate rather
than many complex forces operating. The small size of the country, long colonial
history, simple economic and political organization, dual economy etc. are the factors
leading to the development of city primacy. Bangkok (Thailand), Lagos (Nigeria),
Harare (Zimbabwe) etc. are some examples of the primate city.
Binary Deviation
Binary deviation emerges when the population of the second-largest city is more
than half the population of the largest city. This situation is observed when a number
of cities of almost similar size dominate the upper end of the hierarchy (Fig. 2.40).
The high rate of industrialization, presence of more than one national identity, long
history of urbanization etc. are the factors responsible for binary deviation in the
rank-size relationship. For example, Madrid and Barcelona in Spain; Mumbai, Delhi
and Kolkata in India.
Stepped Pattern Deviation
In stepped pattern deviation, not one but a number of cities may be observed at every
level, each city resembling the others in population size and functioning (Fig. 2.40).
2.5 Types of Graphical Representation of Data 123
Fig. 2.40 Deviations in rank-size distribution
2.5.4.10 Box Plot (‘Box-And-Whiskers’) Graphs
The concept of box-and-whiskers graph was first given by John Tukey in 1970. A
box plot, also known as box-and-whisker plot, is an important graphical method to
represent the spread and centres of a data set. Measures of spread consist of the
inter-quartile range and the mean, whereas the measures of the centre include the
average or mean and median (the middle-most value) of a data set. Box-and-whisker
plot is a data display that allows seeing many attributes of a distribution at a glance,
i.e. they can be a useful means for getting a quick summary of the data set.
Elements of a Box-And-Whisker Plot
Box plot is a convenient method for the graphical depiction of groups of numerical
data using five number summaries: the minimum, the maximum, the median, the
lower quartile and the upper quartile (Figs. 2.41 and 2.42).
1. Minimum: It is the lowest value in the data set excluding outliers, if any and
shown at the far left of the plot, i.e. at the end of the left ‘whisker’.
2. Maximum: It is the largest value in the data set excluding outliers, if any and
shown at the far right of the right ‘whisker’.
3. Median (Q2): It is the middle-most value of the data set and is represented as
a line at the centre (middle) of the box.
124 2 Representation of Geographical Data Using Graphs
Fig. 2.41 Box-and-whisker graph without outliers
Fig. 2.42 Box-and-whisker graph with outliers
4. First (lower) quartile (Q1): It is the middle value between the smallest number
(not always the minimum) and the median (Q2) of the data set and is shown at
the far left of the box, i.e. at the far right of the left ‘whisker’.
5. Third (upper) quartile (Q3): It is the middle value between the largest number
(not always the maximum) and the median (Q2) of the data set and is shown at
the far right of the box, i.e. at the far left of the right ‘whisker’.
2.5 Types of Graphical Representation of Data 125
6. Inter-quartile range (IQR): It is the distance between the lower and upper
quartile.
IQR = Q3−Q1 = qn(0.75)−qn(0.25) (2.34)
Methods of Construction
In constructing this graph, at first we draw an equal interval scale and using this scale,
a rectangular box is drawn with one end at the lower quartile (Q1) and the other end
at the upper quartile (Q3). Then we draw a vertical line at the median value, i.e. at the
second quartile (Q2). A distance of 1.5 times the IQR is measured out from the right
of the upper quartile and a horizontal line is drawn up to the larger observed value
from the given data set that falls within this distance. In the same way, a distance of
1.5 times the IQR is measured out from the left of the lower quartile and a horizontal
line is drawn up to the lower observed value from the data set that falls within this
distance. These two horizontal lines or segments are called the ‘whiskers’ (Figs. 2.41
and 2.42). All other observed values are plotted as outliers.
The spacing between different divisions of the box specifies the amount of disper-
sion or spread (degree of heterogeneity) and skewness (degree of symmetry or
asymmetry) in the data set, and gives an idea about outliers.
Example Without Outliers
The monthly rainfall of 24 months was measured in mm and the values are given
below:
52, 52, 52, 53, 58, 61, 61, 62, 62, 63, 64, 65, 65, 65, 66, 67, 68, 70, 70, 71, 72, 73,
74 and 76.
A box-and-whisker plot can be constructed by calculating the five number
summaries: minimum, maximum, median, lower quartile and upper quartile.
The minimum is the smallest number in the given rainfall data set. Here, the
minimum monthly rainfall is 52 mm.
The maximum is the largest number in the given rainfall data set. Here, the
maximum monthly rainfall is 76 mm.
The median is the middle value of the ordered rainfall data set. This means that
exactly 50% of the rainfall values are less than the median and 50% of the rainfall
values are greater than the median rainfall. So, the median rainfall of the given data
set is 65 mm.
The lower quartile is a value in which exactly 25% of the values are less than
this and 75% of the values are greater than this value. It can be easily calculated by
finding the middle value between the minimum value and the median value. In this
given data set, the value of the lower quartile (middle value between 52 and 65 mm)
is 61 mm.
126 2 Representation of Geographical Data Using Graphs
The upper quartile is a value in which exactly 75% of the values are less than
this and 25% of the values are greater than this value. It can be easily calculated by
finding the middle value between the median value and the maximum value. In this
given data set, the value of the upper quartile (middle value between 65 and 76 mm)
is 70 mm.
The inter-quartile range (IQR) can be calculated using Eq. 2.34:
IQR=Q3−Q1= 70 mm−61 mm = 9 mm
Hence, 1.5 IQR 1.5 IQR = 1.5 × 9 mm = 13.5 mm
1.5 IQR after (above) the upper quartile is
Q3+1.5 IQR=70 mm+13.5 mm =83.5 mm
1.5 IQR before (below) the lower quartile is
Q1−1.5 IQR= 61 mm−13.5 mm = 47.5 mm.
Here, the maximum rainfall in the data set is 76 mm and 1.5 IQR after (above)
the upper quartile is 83.5 mm which indicates that the largest data set value is lower
than 1.5 IQR after (above) the upper quartile. Therefore, the upper whisker will be
drawn at the maximum rainfall value, i.e. 76 mm.
In the same way, the minimum rainfall in the data set is 52 mm and 1.5 IQR
before (below) the lower quartile is 47.5 mm, which indicates that the smallest data
set value is greater than 1.5 IQR before (below) the lower quartile. Therefore, the
lower whisker will be drawn at the minimum rainfall value, i.e. 52 mm (Fig. 2.41).
Example with Outliers
The above example is without outliers. But in this example outliers are incorporated
by changing the first and last values of rainfall (in mm).
47, 52, 52, 53, 58, 61, 61, 62, 62, 63, 64, 65, 65, 65, 66, 67, 68, 70, 70, 71, 72, 73,
74 and 84.
As all the values except the first and last values remain unchanged, the median,
lower quartile and upper quartile remain the same.
In this data set, the maximum rainfall value is 84 mm and 1.5 IQR after (above)
the upper quartile is 83.5 mm, which indicates that the maximum rainfall is larger
than 83.5 mm. So, the maximum rainfall value (84 mm) is an outlier. Therefore,
the upper whisker will be drawn at the greatest rainfall value smaller than 83.5 mm,
which is 74 mm.
In the sameway, the minimum rainfall value is 47mm and 1.5 IQR before (below)
the lower quartile is 47.5 mm, which indicates that the minimum rainfall is smaller
than 47.5 mm. So, the minimum rainfall value (47 mm) is an outlier. Therefore, the
2.5 Types of Graphical Representation of Data 127
lower whisker will be drawn at the smallest rainfall value largerthan 47.5 mm, which
is 52 mm (Fig. 2.42).
2.5.4.11 Hypsometric Curve or Graph
Hypsometric (also called hypsographic) curve or graph is an important form of
cumulative frequency curve or an Ogive. It is obtained by plotting the height of the
contour with respect to the corresponding proportions of a specified unit area of
the earth’s surface (say a drainage basin) (Pal 1998). Hypsometry, first described by
Strahler (1952), involves the measurement and analysis of the relationship between
height and basin area to understand the degree of dissection and stage of the cycle of
erosion. The basic data required for the study of area–height relationship are areas
between successive contours and their respective heights. The area may be measured
with the help of planimeter or may be estimated by the intercept method. The height
is obtained from the contour map.
Area–height graph indicate actual areas between two successive contours and
therefore the horizontal axis represents the area in terms of percentage of total area
and the vertical axis represents the height. Hypsometric graph is generally used to
show the proportion of the area of the surface at various elevations above or below a
datum and thus the values of the area are plotted as ratios of the total area of the basin
against the corresponding heights of the contours and hence the area is represented
by cumulative proportion or percentage. A hypsometric curve is basically a graph
representing the proportion of land area that exists at different heights by plotting
relative area with respect to relative height.
On our earth, the heights can take on either positive (above sea level) or negative
(below sea level) values and are bi-modal due to the contrast between the continents
and oceans. Hypsometry of the earth reveals that earth has two peaks in height, one
for the continents and the other for the ocean floors (Fig. 2.43).
From Table 2.28, it is clear that the total area of the whole basin (A) is 4830 km2
and the maximum height of the basin (H) is 575 m. The area–height relationship
of the basin (Fig. 2.44) can be expressed dimensionlessly by computing the relative
area (the ratio between the individual area between successive contours, ai and the
whole area of the basin, A) and the relative height (the ratio of the mid-value of the
contour height, hi to the maximum height of the drainage basin, H). These ratios are
computed in Table 2.28 and represented on graph as shown in Figs. 2.45 and 2.46.
Although the hypsometric curve representing the relation between the proportions
of area (shown on x-axis or abscissa) and height (shown on y-axis or ordinate)
essentially pass through X = 0, Y = 1 and X = 1, Y = 0 but its location on graph is
a function of the stage of erosion of the basin concerned.
128 2 Representation of Geographical Data Using Graphs
Fig. 2.43 Hypsometric curve for the whole earth
Table 2.28 Calculations for area–height graph and hypsometric curve in a sample drainage basin
(Fig. 2.44)
Class intervals
for height in
metres
Mid value (hi )
in metres
Area between
contours in sq.
km.(ai )
hi
H
ai
A Cumulative
up: less than
ai
A
ai hi
<200 175 130 (2.69%) 0.30 0.027 0.027 22,750
200–250 225 260 (5.38%) 0.39 0.054 0.081 58,500
250–300 275 680 (14.08%) 0.48 0.141 0.222 187,000
300–350 325 1230 (25.47%) 0.56 0.255 0.477 399,750
350–400 375 1080 (22.36%) 0.65 0.224 0.701 405,000
400–450 425 760 (15.73%) 0.74 0.156 0.857 323,000
450–500 475 420 (8.70%) 0.83 0.087 0.944 199,500
500–550 525 120 (2.48%) 0.91 0.025 0.969 63,000
> 550 Say 575 150 (3.11%) 1.00 0.031 1.00 86,250
Total H = 575
∑
ai = 4830
km2 (= A)
∑
ai hi =
1,744,750
Hypsometric Integral (HI)
Hypsometric integral (HI) is the ratio of the volume or percentage of the total volume
of the basin area below the curve (Fig. 2.46) and thus it indicates the volume of the
basin area unconsumed by the dynamic wheels of erosion whereas erosion integral
(EI) is a proportionate area above the curve and thus it reveals the volume of basin
area which has already been consumed by the erosional processes. Thus hypsometric
integral is the ratio between the area of the surface below the hypsometric curve (it
2.5 Types of Graphical Representation of Data 129
Fig. 2.44 Sample drainage basin showing height and area
Fig. 2.45 Area–height relationship of the given drainage basin
130 2 Representation of Geographical Data Using Graphs
Fig. 2.46 Hypsometric curve of the given drainage basin
is between 0 and 1) and the area of the whole square (here it is 1). Theoretically, the
value of hypsometric integral ranges between 0 and 1.
Though the value of hypsometric integral can be calculated using different
techniques, the following techniques are very popular and widely accepted.
(1) Elevation–relief ratio (E) relationship method: When the spot heights of
several numbers of places are known to us then the value of hypsometric
integral is calculated using the following equation:
E ≈ H I = Elmean − Elmin
Elmax − Elmin
(2.35)
where E is the elevation–relief ratio equivalent to the hypsometric integral (H I );
Elmean is the weighted mean elevation of the entire drainage basin; Elmax and Elmin
are the maximum and minimum elevations of the drainage basin, respectively.
The weighted mean height of the drainage basin is calculated using the following
formula:
hc =
∑
ai hi∑
ai
(2.36)
where hc is the mean height of the drainage basin. In the given example (Table 2.28
and Fig. 2.44),
∑
ai hi = 1,744,750 and
∑
ai = 4830. So, the mean height of the
drainage basin (hc) = 1744750
4830 = 361.23 m.
2.5 Types of Graphical Representation of Data 131
The value of Elmax and Elmin are 575 m and 175 m, respectively, then
E ≈ H I = 361.23 − 175
575 − 175
= 186.23
400
= 0.4655
Hence, the value of hypsometric integral is 0.4655.
(2) When co-ordinates of the points define the hypsometric curve (x, y;
x = ai
A and y = hi
H
)
(Fig. 2.46), HI is found using the following equation:
H I =
∣∣∑ xi yi+1 − ∑
yi xi+1
∣∣
2
(2.37)
(3) Mathematically, the hypsometric integral can be found from the integral
calculus as integral
f = Volume
Total height × Total area
1.0∫
0.0
a.Δh (2.38)
where a is area and Δh is the range in height h.
Importance of Hypsometric Curve and Hypsometric Integral
The value of hypsometric integral has been accepted as an important morphometric
indicator of the stage of erosion of the basin. According to Strahler (1952), a high
integral value exceeding 0.60 indicates the youthful stage in the development of
drainage basin (denudation processes are not keeping pacewith the rate of upliftment,
i.e. much of the rock volume in the basin is still to be eroded); the value in between
0.35 and 0.60 indicates the mature or equilibrium stage and the value less than 0.35
indicates the old erosional surface or monadnock stage of the basin (Fig. 2.47).
The hypsometric integral is a dimensionless parameter and hence allows different
drainage basins to be compared irrespective of scale. The shape of hypsometric curve
and the value of hypsometric integral act as important indicators of basin conditions
and characteristics. Hypsometric integral values are associated with the degree of
disequilibrium in the balance between tectonic forces and the degree of erosion.
Hypsometric integral is considered the most useful technique for the study of active
tectonics.
A useful aspect of the hypsometric curve is that drainage basins having different
sizes can be easily compared with each other since an area elevation is represented as
132 2 Representation of Geographical Data Using Graphs
Fig. 2.47 Understanding the stages of landform development using hypsometric curve
functions of total area and total elevation, i.e. the hypsometric curve is independent
of variations in basin size and relief (Alhamed and Ahmad Ali 2017).
It may be noted that the low value of hypsometric integral (below 0.30) is only
sustained as long as few monadnocks give a relatively large differencein height
between the highest and the lowest places. But when the monadnocks are eroded, the
integral returns to about 0.40–0.60. It may be pointed out that hypsometric integral is
a very delicate morphometric measure and hence it should be used with the greatest
care and field verifications, otherwise it may render ambiguous results.
2.5.5 Frequency Distribution Graphs
2.5.5.1 Histogram
Themost common and simple form of graphical representation of grouped frequency
distribution is the histogram. It is constituted by a set of adjoining rectangles drawn
on a horizontal baseline, having areas directly proportional to the class frequencies
(Das 2009). Generally, the class boundaries are shown along the x-axis (abscissa)
and the numbers of frequencies are represented along the y-axis (ordinate). As the
class boundaries are taken into account to represent the rectangles, these become
continuous to each other.
In constructing a histogram, the fundamental principle is that the area of each
rectangle is directly proportional to the class frequency ( fi ). Hence,
2.5 Types of Graphical Representation of Data 133
Area of a rectangle (A) ∞ fi (2.39)
or
hi × wi = k. fi [Area of a rectangle (A) = height × width] (2.40)
where hi is the height of the rectangle for the i th class;wi is the width of the rectangle
for the i th class; k is constant of proportionality.
or
hi = k
wi
fi (2.41)
Equation 2.41 has distinctive applications on grouped frequency distribution with
equal class size and unequal class size like (Sarkar 2015).
Grouped Frequency Distribution with Equal Class Size
In a grouped frequency distribution where all the classes are of equal size (wi ),
Eq. 2.41 becomes
hi =
(
k
w
)
fi (2.42)
or
hi = ki × fi ; [ki = k
w
= constant because all the classes have equal size]
(2.43)
that is
hi ∞ fi (2.44)
So, in the case of the frequencydistributionhaving the sameclass size, the height of
each rectangle is directly proportional to its class frequency and it is then customary to
take the heights numerically equal to the class frequencies (Table 2.29 and Fig. 2.48).
Grouped Frequency Distribution with Unequal Class Size
In a grouped frequency distribution where the classes are of different sizes (wi ),
Eq. 2.41 becomes
134 2 Representation of Geographical Data Using Graphs
Table 2.29 Grouped
frequency distribution with
equal class size (average
concentration of SPM in the
air)
Class boundary Class mark
(xi )
Class width
(wi )
Frequency
( fi )
170.5–220.5 195.5 50 9
220.5–270.5 245.5 50 4
270.5–320.5 295.5 50 2
320.5–370.5 345.5 50 6
370.5–420.5 395.5 50 3
420.5–470.5 445.5 50 1
Fig. 2.48 Histogram (average concentration of SPM in the air)
hi = k
(
fi
wi
)
(2.45)
or
hi = k × fdi [ fdi is the frequency density of the i th class] (2.46)
that is,
hi ∞ fdi (2.47)
2.5 Types of Graphical Representation of Data 135
Table 2.30 Grouped frequency distribution with unequal class size (monthly income of families)
Class boundary
(Monthly income
in Rs.’00)
Class mark (xi ) Class width (wi ) Frequency ( fi )
[no. of family]
Frequency density
( fdi )
[
fi
wi
]
0–50 25 50 40 0.8
50–120 85 70 60 0.86
120–250 185 130 45 0.35
250–350 300 100 35 0.35
350–600 475 250 25 0.1
600–950 775 350 20 0.057
Fig. 2.49 Histogram (monthly income of families)
So, in the case of classes having unequal width, the rectangles will also be unequal
inwidth and thus their heightsmust be directly proportional to the frequency densities
but not to the class frequencies (Table 2.30 and Fig. 2.49). Therefore, in unequal class
size, the rectangles of the histogram must be drawn with respect to the frequency
densities of the classes.
136 2 Representation of Geographical Data Using Graphs
Uses of Histogram
1. A series of rectangles or a histogram gives a visual description of the relative
size of different groups of a data series. The entire distribution of total frequency
into different classes becomes easy to understand at a glance.
2. The surface structure of the top of the rectangles gives an approximate idea
about the nature (average, spread and shape etc.) of the frequency distribution
and the frequency curve.
3. It is generally used for the graphical representation of mode.
4. Numerous geographical, economical and social data can be easily represented
by histogram for their better and fruitful understanding.
2.5.5.2 Difference Between Historigram and Histogram
Historigram and histogram are two important methods of graphical representation
of statistical or geographical data. The major differences between these two are as
follows:
Historigram Histogram
1. Representation of classified and summarized
time series data by line is called historigram
1. Histogram is a set of adjoining rectangles
drawn on a horizontal baseline
2. It represents the change of values of different
variables with time
2. It represents the distribution of frequencies
(number of observations) in different
measurement classes
3. In historigram, time (year, month, day etc.) is
shown along the x-axis and the values of the
variable are shown along the y-axis
3. In histogram, the class boundaries are shown
along the x-axis (abscissa) and the numbers of
frequencies are shown along the y-axis
(ordinate)
4. It is used to understand the temporal changes
of uni-variate data and to compare the changes
of two or more variables with time
4. It is used to understand the nature of the
frequency distribution, drawing of frequency
polygon and frequency curve, estimation of the
value of mode etc.
2.5.5.3 Frequency Polygon
Frequency polygon is the graphical portrayal of grouped frequency distribution alter-
native to histogram andmay be looked upon as it is derived from histogram by joining
the mid-points of the tops of successive rectangles by straight lines. In construction,
the frequency polygon is obtained by joining the consecutive points by straight lines
whose abscissae indicate the classmark (xi ) and ordinates indicate the corresponding
class frequencies ( fi ) (Figs. 2.50, 2.51, 2.52 and 2.53).
Two main assumptions for constructing polygon are:
2.5 Types of Graphical Representation of Data 137
Fig. 2.50 Frequency
polygon showing the average
concentration of SPM in the
air
Fig. 2.51 Frequency
polygon showing the
monthly income of families
(i) All the values in a particular class are uniformly distributed within the whole
range of the class interval. Thus the class mark (xi ) is considered to be the
representative of the corresponding class.
(ii) For the same frequency distribution, the area covered by the histogrammust be
equivalent to the area enclosed within the frequency polygon. In this purpose,
the two endpoints of the polygon are joined by straight lines to the abscissa
at the mid values (class marks, xi ) of the empty classes at each end of the
frequency distribution (Figs. 2.50, 2.51, 2.52 and 2.53).
Frequency polygon may be plotted separately and individually as well as on
the histogram (Figs. 2.52 and 2.53). In the case of the distribution with unequal
138 2 Representation of Geographical Data Using Graphs
Fig. 2.52 Histogram with
polygon showing the average
concentration of SPM
(mg/m3) in the air
Fig. 2.53 Histogram with polygon showing the monthly income of families
classes, the polygon is drawn by plotting the frequency density ( fdi ) instead of
simple frequency ( fi ) against the class mark (xi ) (Figs. 2.51 and 2.53).
2.5 Types of Graphical Representation of Data 139
Fig. 2.54 Frequency
polygon of discrete variable
(Distribution of landslide
occurrences)
Uses of Frequency Polygon
The frequency polygon is especially useful in representing simple frequency distri-
bution of any discrete variable. For example, day-wise distribution of number of land-
slide occurrences can effectively be represented in a frequency polygon (Fig. 2.54).
It gives us a better idea about the distribution of observations in different classes and
the shape of the frequency curve.
2.5.5.4 FrequencyCurve
In a generic sense, frequency curve is the modified form of histogram and frequency
polygon. In drawing histograms, it is assumed that the observations (frequencies) are
homogeneously distributed all through the range of valueswithin the class boundaries
of any class, but this may not be always true. Actually, a histogram provides the
approximate idea about the nature and pattern of distribution of a limited number of
frequencies (no. of observations) in different classes. The widths of the classes of
the frequency distribution could be made smaller, but the problem is that some of
the classes may remain empty (classes without any class frequency) and the actual
pattern of the distribution of observations in the population will not be understood.
140 2 Representation of Geographical Data Using Graphs
Fig. 2.55 Frequency curve
showing the average
concentration of SPM
(mg/m3) in the air
But if the number of observations is very large, the situation will improve and all the
classes are expected to have some number of frequencies, even when the widths of
the classes are significantly small.
If the class width becomes smaller and smaller along with an indefinite increase
of the total frequency, then the histogram and the frequency polygon tend to move
towards a smooth curve called frequency curve (Das 2009). Generally, it is stated
that in the frequency curve, the points obtained from the plotting of class frequency
( fi ) or frequency density ( fdi ) against the class mark (xi ) are joined by a smooth
curve instead of a series of straight lines (Figs. 2.55 and 2.56). Frequency curve
represents the probability distribution of the variables in the population along with
its area enclosed by the ordinate (‘y’-axis) at two specified points on the abscissa
(‘x’-axis) indicating the probability of lying a value of the variable between these
two extremes. Like histogram and frequency polygon, frequency curve is also an
area graph.
Based on their shape and characteristics, frequency curve is of four types (Das
2009):
(i) Symmetrical bell-shaped or normal curve (Fig. 2.57a), (ii) Asymmetrical
single-humped (Fig. 2.57b), (iii) J-shaped curve (Fig. 2.57c) and (iv) U-shaped curve
(Fig. 2.57d).
Shape of the Frequency Curve
The shape of the frequency curve is very important as it represents the actual nature of
a frequency distribution. It is generallymeasured in terms of two geometric properties
of a frequency curve—(1) Symmetry or asymmetry (skewness) and (2) peakedness
(kurtosis).
2.5 Types of Graphical Representation of Data 141
Fig. 2.56 Frequency curve showing the monthly income of families
Fig. 2.57 Types of frequency curve
142 2 Representation of Geographical Data Using Graphs
Fig. 2.58 Positive, negative and zero or no skewness
Skewness (Sk)
An important property of the shape of a frequency curve is whether it has one peak
(unimodal) or more than one (bi-modal or multimodal). If it is unimodal (one peak),
like most data sets, emphasis should be given to know whether it is symmetrical
or asymmetrical in shape. Skewness measures the symmetry, or more accurately, the
lack of symmetry of the frequency curve. Skewness signifies the extent of asymmetry
of the frequency curve and is of three types:
(a) Positive skewness
If most of the observations in a data set are located at the left of the curve (peak is
towards the lower class boundaries) and the right tail is longer, then the distribution
is said to be skewed right or positively skewed. In a positively skewed frequency
distribution or curve, the relation between three measures of central tendency is
mean > median > mode, i.e. the value of mean is greater than the median and
again the value of median is greater than the mode (Fig. 2.58).
(b) Negative skewness
If most of the observations in a data set are located at the right of the curve (peak is
towards the upper-class boundaries) and the left tail is longer, then the distribution
is said to be skewed left or negatively skewed. In a negatively skewed frequency
distribution or curve, the relation between three measures of central tendency is
mean < median < mode, i.e. the value of mean is lower than the median and again
the value of median is lower than the mode (Fig. 2.58).
(c) Zero or no skewness or symmetric
A frequency distribution or curve is said to be symmetrical in nature when the
values are uniformly distributed around the mean. In such conditions the curve
looks identical to the left and right of the central point. In a symmetrical or zero
2.5 Types of Graphical Representation of Data 143
skewed frequencydistribution or curve, the relation between threemeasures of central
tendency is mean = median = mode, i.e. the values of mean, median and mode
are equal (Fig. 2.58).
Skewness can be measured in different methods:
(1) Pearson’s first measure
Skewness = Mean − Mode
Standard deviation
(2.48)
(2) Pearson’s second measure:
Skewness = 3(Mean − Median)
Standard deviation
(2.49)
(3) Bowley’s measure:
Skewness = Q3 − 2Q2 + Q1
Q3 − Q1
(2.50)
where Q1, Q2 and Q3 are lower, middle and upper quartiles, respectively.
(4) Moment measure of skewness is called skewness coefficient, β1 (read as beta-
one):
Skewness coe f f icient(β1) = μ3
σ 3
(2.51)
where μ3 is the third central moment and σ is the standard deviation.
μ3 =
∑n
i=1,2....(xi − x)3
N
(for ungrouped data) (2.52)
μ3 =
∑n
i=1,2.... fi (xi − x)3
N
(for grouped data) (2.53)
In statistics, ‘moment’ (μ) is the mean of the first power of the deviation, i.e. the
spacing of the size class or individual item in the frequency distribution from the
mean, adding them up and dividing them by the total size of the distribution. This is
the first moment (μ1) about the mean which is symbolically written as
μ1 =
∑|xi − x |
N
(2.54)
Higher moments (μ2, μ3, μ4 etc.) can be defined in the sameway. In symmetrical
frequency distribution bothμ1 andμ2 are zero (0), so the skewness coefficient would
also be zero (0).
144 2 Representation of Geographical Data Using Graphs
According to Pearson’s measures, there are no theoretical limits of skewness. But
generally the value lies between +3 and −3. According to Bowley’s measurement,
the value of skewness ranges between +1 and −1.
Normal distribution (Normal Curve)
Normal distribution, also called Gaussian distribution (after the name of the mathe-
matician Gauss), is a continuous probability distribution and is defined by the prob-
ability density function, f (x) which is the height (Y ) of the normal curve above the
baseline at a given point (xi ) along the measurement scale of the random variable, x
itself (Pal 1998). The model used to obtain the desired probabilities is
Y = f (xi ) = 1
σx
√
2π
e
− 1
2
(
xi −μ
σ
)2
(2.55)
where e is the exponent (2.71828), π is the mathematical constant (3.14159), μ and
σ are the population mean and standard deviation, respectively, xi is any value of the
continuous random variable (−∞ < xi < +∞).
In other words, a frequency distribution having skewness = 0 (Sk = 0) is called
a normal probability distribution. The probability curve of the normal distribution
is called normal curve. The curve is symmetrical and bell-shaped (Figs. 2.58 and
2.59) and the two tails extend to infinity on either side. In the real world, many
actual distributions like rainfall data for any raingauge station collected over a large
number of years (assuming no climatic change) tends to develop normal frequency
distribution with a ‘bell-shaped’ symmetrical curve. This symmetry means that the
height of the normal curve is the same if one moves equal distances to the left and
right of the mean. The highest frequencies in this curve are around the mean and the
frequency decreases as the distance from the mean increases. If we know the value
of μ and σ , it is possible to determine the estimates of Y function for constructing
the normal curve and calculating the area under the curve of any interval of xi (Table
2.31).
Computation of the value of Yfor every value of xi is tedious and hence the
position of any particular observation (say a score xi ) may be expressed relative to
other scores in the data set by getting itself transformed to a standardized normal
random variable known as ‘standard score’ or a ‘z-score’ (read as ‘zee’) where
z = xi − μ
σ
= Critical value − Mean
Standard deviation
(2.56)
If all of the raw values in a distribution are converted to standard or z-scores, we
get a new standardized distribution always having a ‘mean, μ equal to zero (0)’ and
a ‘standard deviation, σ equal to one (1)’. This is a useful transformation known as
standardization which results in new values for the individuals. As the normal curve
is symmetrical about the mean, half of the area under the curve lies on each side
2.5 Types of Graphical Representation of Data 145
Fig. 2.59 Area under a standard normal curve
Table 2.31 Methods of calculating Y in f (x) for constructing a normal curve
xi (rainfall in
cm) [μ =
50 cm and σ =
10 cm]
1
σ
√
2π
xi −μ
σ
( xi −μ
σ
)2 − 1
2
( xi −μ
σ
)2
e
− 1
2
(
xi −μ
σ
)2
Y (see Eq. 2.55)
25 0.03989 −2.50000 6.25000 −3.12500 0.04393 0.00175
45 0.03989 −0.50000 0.25000 −0.12500 0.88249 0.03520
50 0.03989 0.00000 0.00000 0.00000 1.00000 0.03989
65 0.03989 1.50000 2.25000 −1.12500 0.32465 0.01295
75 0.03989 2.50000 6.25000 −3.12500 0.04393 0. 00175
of the mean. This reveals that in a frequency distribution approximating the normal
curve, 50% of the values will be less than the mean and 50% will be greater than the
mean (Fig. 2.59).
Properties of Normal Curve
Normal curve has a number of interesting properties. These include:
146 2 Representation of Geographical Data Using Graphs
(i) Normal curve (normal distribution) has two important parameters μ and σ ,
μ = mean and σ = standard deviation. In some literature works, μ is also
used as x .
(ii) The normal curve is always ‘bell-shaped’ and unimodal in nature.
(iii) It is symmetrical about its centre (the line x = μ) and mean occupies the
centre. The vertical line drawn through the mean divides the curve into two
equal halves. Thus, 50% of the values are less than the mean and 50% are
greater than the mean.
(iv) The values obtained from the addition or subtraction of the normally
distributed values are also normally distributed.
(v) Three measures of central tendencies are equal in value (i.e. mean = median
= mode = μ), so on curve they coincide with each other.
(vi) Normal curve has two points of inflections (the pointwhere the curve changes
curvature) at a distance of±σ on either side of themean (μ). Thus, the normal
curve is convex upward in the interval (μ − 1σ and μ + 1σ) and concave
upward outside this interval.
(vii) Two tails of a normal curve are asymptotic to the x-axis or horizontal axis, i.e.
if two tails of a normal curve are extended in both the directions to infinity,
they never cut the x-axis.
(viii) The form of the normal curve in terms of its shape (skewness) and height
(kurtosis) depends on the mean and the standard deviation.
(ix) The percentage distribution of the area under a standard normal curve is
(Table 2.32 and Fig. 2.59):
(a) 68.26% (68%) between μ ± 1σ
(b) 95.44% (95%) between μ ± 2σ
(c) 99.74% (99%) between μ ± 3σ
So, almost all the values of x will lie between the limits μ ± 3σ , i.e. mean ±
3(S · D.).
Kurtosis
In a frequency curve, it is required to know the ‘convexity of the curve’ which is
‘kurtosis’ (Greekwordmeaning thereby ‘bulkiness’). Twoormore sets of data having
an equal average, spread and symmetry but may differ in respect of their degree of
peakedness. Kurtosis measures the degree of peakedness or convexity of a frequency
curve, i.e. the extent to which values are concentrated in one part of the curve. It
explains whether the distribution in the data set is having an excessively large or
small number of values (observations) in the intermediate ranges between the mean
and the extreme values and thus resulting in a peakedness or flat-toppedness of the
frequency curve.
Kurtosis is the fourth moment about the mean, μ4. According to Pearson, it is a
coefficient, the kurtosis coefficient, β2 (read as beta-two). Kurtosis coefficient (β2)
2.5 Types of Graphical Representation of Data 147
Table 2.32 Standard normal distribution table
STANDARD NORMAL DISTRIBUTION (Values represent area to the left of the Z score)
(The left column stands for the first decimal value of z and the top row stands for the second
decimal value of z)
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9867 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
(continued)
148 2 Representation of Geographical Data Using Graphs
Table 2.32 (continued)
STANDARD NORMAL DISTRIBUTION (Values represent area to the left of the Z score)
(The left column stands for the first decimal value of z and the top row stands for the second
decimal value of z)
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
is obtained using the following formula:
β2 = μ4
μ2
2
(2.57)
Simply it can be written as
β2 = μ4
σ 4
(2.58)
where μ4 is thefourth central moment and σ is the standard deviation.
μ4 =
∑n
i=1,2....(xi − x)4
N
(for ungrouped data) (2.59)
μ4 =
∑n
i=1,2.... fi (xi − x)4
N
(for grouped data) (2.60)
Since kurtosis indicates the spread of the frequency curve, it is determined as
Kurtosis measure, K = Mean − Median
Standard deviation
(2.61)
For a symmetrically distributed curve, as the mean and median coincides with
each other, the kurtosis measure, K should be zero and the kurtosis coefficient, β2
should be 3.0, i.e. K = β2 − 3, where with K = 0, β2 becomes 3.0. Based on the
peakedness of the frequency curve, three types of curves are identified:
(1) Leptokurtic (Positive kurtosis): When β2 > 3 and K > 0, then the curve is
more peaked than the perfect symmetrical curve and it is knownas ‘leptokurtic’,
i.e. the curve with a narrower central position and a higher tail than a perfect
symmetrical curve (Fig. 2.60).
2.5 Types of Graphical Representation of Data 149
Fig. 2.60 Degree of
peakedness (Kurtosis) of
frequency curve
(2) Platykurtic (Negative kurtosis): When β2 < 3 and K < 0, then the curve
is less peaked (more flat) and it is known as ‘platykurtic’, i.e. the curve with
a broader central portion and a lower tail than the perfect symmetrical curve
(Fig. 2.60).
(3) Mesokurtic (Normal curve): From the kurtosis point of view, the perfect
symmetrical curve is the curve having β2 = 3 and K = 0 and it is known as
‘mesokurtic’ (Fig. 2.60).
Uses of Frequency Curve
(i) Different measures of central tendency and dispersion can be easily plotted
on it.
(ii) Plotting of frequency curves on the same base becomes effective to compare
sets of data series.
(iii) The curve is also helpful to determine the normality of a data set.
2.5.5.5 Cumulative Frequency Polygon and Curve (Ogive)
The graphical representation of cumulative frequencies in a frequency distribution is
called cumulative frequency polygon. For the drawing of this graph, the cumulative
frequencies are plotted along the ‘Y ’-axis against the corresponding class boundaries,
plotted along the ‘X’-axis and the obtained points are joined by straight lines and this
line is known as cumulative frequency polygon. Generally, two distinctive polygons
are drawn: (i) Less than type and (ii) more than type.
(i) Less than type: Less than type polygon is drawn based on the less than type
cumulative frequencies (Tables 2.33 and 2.34). It begins from the lowest class
boundary on the horizontal axis (abscissa or ‘X’-axis), continues to rise upward
150 2 Representation of Geographical Data Using Graphs
Table 2.33 Worksheet for drawing Ogive (with equal class size)
Class boundary Frequency (f i) Cumulative frequency (F)
Less than F More than F
170.5–220.5 9 170.5 0 170.5 25
220.5–270.5 4 220.5 9 220.5 16
270.5–320.5 2 270.5 13 270.5 12
320.5–370.5 6 320.5 15 320.5 10
370.5–420.5 3 370.5 21 370.5 4
420.5–470.5 1 420.5 24 420.5 1
N = ∑
fi = 25 470.5 25 470.5 0
Table 2.34 Worksheet for drawing Ogive (with unequal class size)
Class boundary Frequency ( fi ) Cumulative frequency (F)
Less than F More than F
0–50 40 0 0 0 225
50–120 60 50 40 50 185
120–250 45 120 100 120 125
250–350 35 250 145 250 80
350–600 25 350 180 350 45
600–950 20 600 205 600 20
N = ∑
fi = 225 950 225 950 0
and ends at the highest class boundary corresponding to the total frequency
(N) of the distribution. The less than polygon looks like a broad and elongated
S-shape.
(ii) More than type: Contrary to less than type polygon, it is drawn based on more
than type cumulative frequencies (Tables 2.33 and 2.34). It begins from the
total frequency (N) at the lowest class boundary and progressively descends to
the highest class boundary on the horizontal axis (abscissa or ‘X’-axis). More
than type polygon looks like a broad, elongated but inverted letter S.
Cumulative frequency curve is themodified formof cumulative frequencypolygon
in which the plotted points are joined by smooth freehand curves as an alternative
of straight lines (Figs. 2.61 and 2.62). The combined representation of less than
type and more than type cumulative frequency curves looks like a wine-glass called
wine-glass curves. A combined representation of less than and more than cumulative
frequency polygons or curves is calledOgive (Figs. 2.61 and 2.62). The two polygons
or curves intersect at the median point of the distribution. The method of graphical
construction of Ogives in frequency distribution with unequal class widths is the
same as in the case of equal widths of the classes in frequency distribution.
2.5 Types of Graphical Representation of Data 151
Fig. 2.61 Cumulative
frequency curve (Ogive)
showing the average
concentration of SPM
(mg/m3) in air
Fig. 2.62 Cumulative
frequency curve (Ogive)
showing the monthly income
of families
Uses of Cumulative Frequency Polygon and Curve (Ogive)
A cumulative frequency curve (Ogive) is more useful than a frequency curve to
understand the content of a frequency distribution. The uses of Ogive include:
(1) As the Ogive is the only graphical representation of the cumulative frequency
distribution, it is very useful to find the values of median, quartiles, deciles and
percentiles graphically.
(2) The number of observations (frequencies) lying below or above a particular
value, in between any two specified values can be easily found from the Ogive.
(3) It is also useful to find out the cumulative frequencies above or below a certain
specified value of the variable.
152 2 Representation of Geographical Data Using Graphs
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ISBN: 81-87461-00-4
Singh VP (1994) Elementary hydrology. Prentice Hall of India Private Limited, New Delhi
Singh RL, Singh RPB (1991) Elements of practical geography. Kalyani Publishers
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Strahler A (1952) Dynamic basis of geomorphology. Geol Soc Am Bull 63:923–938. https://doi.
org/10.1130/0016-7606(1952)63[923:DBOG]2.0.CO;2
Sutcliffe et al (1981) The water balance of the Betwa basin, India/Le bilan hydrologique du bassin
versant de Betwa en Inde. Hydrol Sci Bull 26(2):149–158. https://doi.org/10.1080/026266681
09490872[J.V.SUTCLIFFE,R.P.AGRAWAL&JULIAM.TUCKER]
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Chapter 3
Diagrammatic Representation
of Geographical Data
Abstract Diagrammaticrepresentation and visualization of geographical data is
very simple, attractive and easy to understand and explain to the geographers as
well as to the common literate people. It helps to explore the nature of data, the
pattern of their spatial and temporal variations and understanding their relationships
to accurately recognize and analyse features on or near the earth’s surface. This
chapter focuses on the detailed discussion of various types of diagrams classified on
a different basis. All types of one-dimensional (bar, pyramid etc.), two-dimensional
(circular, triangular, square etc.), three-dimensional (cube, sphere etc.) and other
diagrams (pictograms and kite diagram) have been discussed with suitable exam-
ples in terms of their appropriate data structure, necessary numerical (geometrical)
calculations, methods of construction, appropriate illustrations, and advantages and
disadvantages of their use. It includes all the fundamental geometric principles and
derivation of formulae used for the construction of these diagrams.A step-by-step and
logical explanation of their construction methods becomes helpful for the readers for
an easy and quick understanding of the essence of the diagrams. Each diagram repre-
sents a perfect co-relation between the theoretical knowledge of various geographical
events and phenomena and their proper practical application with suitable examples.
Keywords Diagrammatic representation · Geometric principles · One-dimensional
diagram · Two-dimensional diagram · Three-dimensional diagram
3.1 Concept of Diagram
Diagram is another important form of visual representation of geographical data in
which importance is laid on the basic facts of one selected element. In the diagram,
data are represented in a very much abstract and conventionalized geometric form.
All types of categorical and geographical data, including time series and spatial series
data, can be easily represented in diagrams. Representation of different geographical
data by suitable diagrams is easy to understand and appreciated by all the people
without having geographical, geometrical and statistical knowledge.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. K. Maity, Essential Graphical Techniques in Geography, Advances in Geographical
and Environmental Sciences, https://doi.org/10.1007/978-981-16-6585-1_3
153
http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-16-6585-1_3&domain=pdf
https://doi.org/10.1007/978-981-16-6585-1_3
154 3 Diagrammatic Representation of Geographical Data
3.2 Advantages and Disadvantages of Data Representation
in Diagrams
Advantages
The advantages of representation of data in diagram are:
(i) Diagram makes the data simple, attractive and impressive, so easily intelli-
gible to all.
(ii) It saves a considerable amount of time, labour and energy.
(iii) Comparison of two or more sets of data becomes possible and easy.
(iv) It has universal utility, i.e. the technique is used all over the world.
(v) It becomes helpful to detect the errors in data if any.
(vi) Various complex data can be easily and simply represented by diagrams.
(vii) It has an immense memorizing effect.
Disadvantages
In spite of all these advantages, representation of data by diagram has some
limitations:
(i) Diagram does not provide a detailed description of data
(ii) Data can’t be represented completely and accurately in a diagram.
(iii) Portrayal of small variation in two ormore sets of data is difficult in a diagram.
(iv) Most of the diagrams are useful to the common people but these are
of little significance to the professionals. Again, some of the diagrams
(three-dimensional or multi-dimensional diagrams) are specifically useful
to professionals and experts.
(v) Depiction of three or more sets of data becomes difficult and impossible in
diagram.
(vi) Diagram does not represent the overall characters of data, rather it signifies
the general conditions only.
(vii) The application of the diagram is very limited in applied research.
3.3 Difference Between Graph and Diagram
Graphs and diagrams are two important techniques for the representation of
statistical as well as geographical data, but major differences between them are as
follows:
3.3 Difference Between Graph and Diagram 155
Graph Diagram
1. Representation of series of data on graph
paper either by means of Cartesian or polar or
oblique co-ordinates on a reference frame is
called graph
1. Representation of data in a highly abstract
and conventionalized geometric form on
two-dimensional plain paper is called diagram
2. Principles of co-ordinate geometry are
applied immensely for the drawing of graphs
2. Some geometrical principles are applied but
co-ordinate geometry is little or insignificantly
applied in diagrams
3. Easy to draw, because it requires only the
knowledge of co-ordinate geometry
3. Drawing of diagrams requires efficiency,
experience and artistic knowledge. Lack of
these will make the diagram less attractive and
impressive
4. Graph depicts the functional or mathematical
relationship between two or more variables
4. Diagram does not depict any functional or
mathematical relationship between variables; it
is used for comparisons only
5. Generally, time series data and frequency
distribution data are appropriately represented
in a graph
5. Diagrams are constructed for representing
categorical data, including time series and
spatial series data
6. Graphs are very much suitable and used for
statistical analysis of geographical data
6. Diagrams are less suitable for the statistical
analysis of geographical data
7. The value of median and mode can be easily
estimated from a graph
7. Median and mode can’t be estimated from a
diagram
8. Graphs are less attractive and impressive to
the eye
8. Diagrams are attractive to the eye and are
better suited for publicity and propaganda
9. In the graph, data are represented by points
or lines
9. In the diagram, data are represented by bars,
pies, rectangles, squares, spheres etc.
3.4 Types of Diagrams in Data Representation
Based on the type and nature of data, the following categories of diagrams can
be distinguished, i.e. statistical diagrams, geographical diagrams and statistical-
geographical diagrams (Sarkar 2015). In addition to this, on the basis of the geometry
of the figures to be constructed, diagrams may be classified into different types from
which the geographers or researchers have to select the most suitable one (Table 3.1).
3.4.1 One-Dimensional Diagrams
It is the diagram in which the size of only one dimension, i.e. length, is considered
to be fixed in proportion to the value of the data it represents.
156 3 Diagrammatic Representation of Geographical Data
Table 3.1 Types of diagrams
3.4.1.1 Bar Diagram
The representation of statistical or geographical data in the form of bars is called
bar diagram. It consists of a number of bars that are equal in width and equally
spaced. The bars are drawn on a common baseline on which the length or height of
the bar is directly proportional to the value it signifies. Based on the constructional
arrangements of the bars, three categories are identified: (i) Vertical or columnar
bar diagram: Bars are drawn vertically above the abscissa (x-axis). (ii) Horizontal
bar diagram: Bars are drawn parallel to the abscissa along the ordinate (y-axis). (iii)
Pyramidal bar diagram: Horizontal bars are arranged in such a way that it forms a
pyramid.
Principles of Construction of bar Diagrams
Though there is no hard and fast rule in constructing bar diagram but some important
principles are followed for drawing it.
1. The bars should be neither too short nor too long. In other words, the bars should
be proportionate in length and breadth.
2. The baseline from which bars are drawn should be clearly shown.
3. The scale should be mentioned clearly and accurately.
4. The intervening space between bars should be equal, i.e. bars should be drawn
at an equal distance from eachother.
5. The bars should be coloured or shaded in order to make them impressive and
attractive.
6. Generally, vertical bars are used to represent the time series data whereas hori-
zontal bars are used to depict the data classified geographically or data classified
by their attributes.
3.4 Types of Diagrams in Data Representation 157
Fig. 3.1 Vertical simple bar (Temporal change of urban population in India since independence)
Source Census of India, 2011
Advantages and Disadvantages of the Use of bar Diagrams
The major advantages and disadvantages of the use of bar diagrams are as follows:
Advantages
1. Drawing and understanding of bar diagram is very simple and easy.
2. A large number of data can be easily represented in bar diagram.
3. Bar diagram can be drawn either vertically or horizontally.
4. It facilitates comparison of different data series.
Disadvantages
1. It is very difficult to represent a large number of aspects of any data in bar
diagram.
2. The drawer fixes the width of the bars arbitrarily.
Types of Bar Diagrams
Simple Bar Diagram
The bar diagram showing only one component or category of data is called simple bar
diagram. In this type each bar represents a single value only (Tables 3.2 and 3.3). It
can be drawn either on a horizontal base (Fig. 3.1) or a vertical base (Fig. 3.2), but bars
on a horizontal base are frequently used. The width of bars must be equal and they
158 3 Diagrammatic Representation of Geographical Data
Fig. 3.2 Horizontal simple bar (Total population in selected states in India) SourceCensus of India,
2011
Table 3.2 Data for vertical simple bar diagram (Temporal changes of urban population in India)
Year Urban population Scale selection Height of each bar (cm)
1951 62,443,709 1 cm to 1,00,000,000 urban
population
0.62
1961 78,936,603 0.79
1971 109,113,977 1.09
1981 159,462,547 1.59
1991 217,177,625 2.17
2001 285,354,954 2.85
2011 361,986,870 3.62
Source Census of India, 2011
should be spaced with equal distance from one another. The scale for constructing
simple bar diagram should be selected based on the highest and lowest values of the
data to be represented.
Example Total population in different states of India, total population in different
years or decades in India, year-wise production of wheat in India, state-wise produc-
tion of rice in India, coal production in different countries in the world etc. can be
represented by simple bar diagram.
3.4 Types of Diagrams in Data Representation 159
Table 3.3 Data for horizontal simple bar diagram (Total population in selected states in India,
2011)
Name of the state Total population (2011) Scale selection Length of each bar (cm)
Uttar Pradesh 199,581,477 1 cm to 50,000,000
population
3.99
Maharashtra 112,372,972 2.24
Bihar 103,804,673 2.08
West Bengal 91,347,736 1.82
Andhra Pradesh 84,665,533 1.70
Madhya Pradesh 72,383,628 1.44
Tamil Nadu 72,138,958 1.44
Source Census of India, 2011
An important limitation of simple bar diagrams is that they can represent only
one component or one category of data. For example, while depicting the total popu-
lation of different states in India, we can depict only the total population but sex-
wise distribution of population in different states can’t be represented in simple bar
diagram.
Multiple Bar Diagram
Bar diagram in which different bars or proportionate lengths are drawn side by side
representing the components is calledmultiple bar diagram (Fig. 3.3). It is generally
used to compare two or more sets of statistical or geographical data (Table 3.4). In
order to discriminate different bars, they are either differently coloured or different
types of crossings or dottings are used in them. Multiple bar diagram is always
equipped with an index or legend to indicate the meaning of different dotting or
colours (Fig. 3.3).
Sub-Divided or Compound Bar Diagram
A compound bar diagram is one in which a single bar is sub-divided into different
parts in proportion to the values given in the data (Fig. 3.4). When the data is
composed of more than one component within a total then compound bar diagram
is used (Table 3.5). The single bar represents the total or aggregate value while the
component parts represent the component values of the aggregate. Sub-divisions in
a bar are distinguished by using different colours or dottings or crossings. A legend
or index is also given to indicate the meaning of different colours or dottings. This
diagram reflects the relation among different components and also between different
components and the aggregate. Compound bar diagram is also known as composite
or component bar diagram.
160 3 Diagrammatic Representation of Geographical Data
Fig. 3.3 Multiple bars showing the continent-wise urban population (%) in 2000 and 2025* Source
UN Population Division, 2009–2010 and The World Guide, 12th ed. * Projected figures
Table 3.4 Calculations for multiple bar diagram (Continent-wise urban population)
Name of the continent Percentage (%) of
urban population
Scale selection Height or length
of each bar (cm)
2000 2025* 2000 2025*
Africa 38.5 49.6 1 cm to 20% urban population 1.92 2.48
Europe 75.0 90.0 3.75 4.5
Anglo America 80.0 86.0 4.0 4.3
Latin America 68.5 75.0 3.42 3.75
Asia 40.0 50.0 2.0 2.5
Oceania 72.5 75.3 3.62 3.76
* Projected figures
Source UN Population Division, 2009–2010 and The World Guide, 12th ed
Percentage Bar Diagram
Percentage bar diagram is a special form of sub-divided bar diagram in which the
value of each component is converted into a percentage (%) of the whole (Fig. 3.5
and Table 3.6). The basic difference between these two bar diagrams is that in the
sub-divided bar diagram the bars are of different heights as their total values may
be different, but in percentage bar diagram bars are equal in height as each bar
3.4 Types of Diagrams in Data Representation 161
Fig. 3.4 Sub-divided bar (Production of different crops in selected years in India) SourceMinistry
of Agriculture and Economic Survey, 2010–2011 and Husain, 2014
Table 3.5 Calculations for sub-divided bar diagram (Production of different crops in India, 1950–
1951 to 2010–2011)
Name of
crops
Production in different time
periods (million tonnes)
Scale
selected
Height of the bar (cm)
1950–51 1970–71 2010–2011 1950–51 1970–71 2010–2011
Rice 30.8 37.6 95.32 1 cm to 40
million
tonnes
0.77 0.94 2.38
Wheat 9.7 18.2 85.93 0.24 0.45 2.15
Pulses 12.5 13.4 28.0 0.31 0.33 0.7
Coarse-grains 15.5 31.4 30.0 0.39 0.78 0.75
Source Ministry of Agriculture and Economic Survey, 2010–2011 and Husain, 2014
represents 100% value (Fig. 3.5). For the data having more than one component,
the percentage bar diagram will be more appropriate and convincing than the sub-
divided bar diagram as the former becomes more helpful in comparison of different
components.
162 3 Diagrammatic Representation of Geographical Data
Fig. 3.5 Percentage bar showing the proportion of population in different age groups in selected
states in India Source Census of India, 2011
Table 3.6 Calculations for percentage bar diagram (Proportion of population in different age
groups in selected states in India, 2011)
Name of the
state
Age-wise (years)
population (%)
Total
(%)
Scale selected Height of the bar (cm) Total
(cm)
0–14 15–59 ≥60 0–14 15–59 ≥60
Uttar Pradesh 33.7 59.5 6.8 100 1 cm to 20%
population
1.68 2.97 0.35 5
Maharashtra 27.2 63.6 9.3 100 1.36 3.18 0.46 5
Bihar 37.3 55.8 7.0 100 1.86 2.79 0.35 5
West Bengal 25.5 66.3 8.2 100 1.27 3.31 0.42 5
Andhra
Pradesh
24.6 66.6 8.8 100 1.23 3.33 0.44 5
Madhya
Pradesh
32.1 60.8 7.1 100 1.60 3.05 0.35 5
Tamil Nadu 23.4 66.1 10.5 100 1.18 3.30 0.52 5
Source Census of India, 2011
3.4 Types of Diagrams in Data Representation 163
3.4.1.2 Pyramids
It is a specific and typical type of bar diagram in which the bars are placed in
such a way that it forms a pyramid-like structure. Pyramid diagrams are popularly
used in different branches of geography including, population studies,urban studies,
ecological or ecosystem studies etc. in different forms for the proper and accurate
representation of geographical data.
Pyramids in Population Studies (Age–sex Pyramid)
In population geography, pyramid is generally used to represent the age–sex compo-
sition of the population (age–sex pyramid) of a country or region. Different age
groups are shown vertically, the base representing the youngest group and the apex
representing the oldest group, whereas the male and female population are shown
horizontally, male population being to the left and female population being to the
right of the pyramid. Generally, age groups are considered to be uniform and hori-
zontal bars of uniform width are drawn. But, if the age groups are unequal then the
width of the bars becomes unequal.
Population pyramids may be drawn in two ways: (i) based on absolute numbers
of the male and female population (Fig. 3.6a) and (ii) the proportion or percentage
of the male and female population with respect to the total (Fig. 3.6b). There are two
possible methods for the conversion of percentage values from absolute numbers of
male and female: First, the numbers of female population in each age group may be
Fig. 3.6 a Absolute population pyramid and b percentage population pyramid
164 3 Diagrammatic Representation of Geographical Data
expressed as the percentage of the total female population of a country or region.
The percentage of male population in each age group may be calculated in the same
way (Table 3.7). Secondly, the male and female population in each age group may
be expressed as the percentage of the total population of a country or region. The
pyramid of absolute numbers shows the size and composition of the population of a
country or region, whereas the pyramid in percentage is used to compare the age–sex
composition of population of two or more countries or regions, on a single scale of
which one is small and the other is big. The work participation status of the male
and female population in different age groups can be easily represented by pyramid
diagram.
Pyramids in Ecological Studies
The use of pyramid diagram is very popular in ecological or ecosystem studies.
The structure and function of successive trophic levels, i.e. producers, primary
consumers, secondary consumers and tertiary consumers may be represented graph-
ically bymeans of ecological pyramids (Sharma 1975). In this pyramid, the producer
(commonly the green plants) constitutes the base of the pyramid (Trophic level-1)
and successive levels or tiers are occupied by the organisms of different consumer
levels making an apex (Fig. 3.7). Based on the number of organisms, biomass and
energy at different trophic levels, ecological pyramids are of three types: (i) Pyramid
of numbers: It portrays the number of organisms at different trophic levels which
commonly decreases from base to apex. (ii) Pyramid of biomass: It represents the
total dry weight of the total amount of living organisms or matters. (iii) Pyramid of
energy: It represents the rate of energy flow and/or productivity at different trophic
levels.
All these ecological pyramids are commonly upright in shape. But, pyramids of
number and biomass are sometimes inverted in shape depending upon the nature and
character of the food chain of a particular ecosystem.
Pyramids in Urban Studies
In urban geography, the absolute numbers or percentage distribution of urban areas
or cities based on different size classes may be represented in the form of a pyramid
(Table 3.8). Here, the number or percentage of cities in each class is plotted horizon-
tally against different size classes of the cities (plotted vertically). Thus symmetrical
horizontal bars are placed on both sides of the size class column forming a pyramid-
like structure (Fig. 3.8). The length of each bar is directly proportional to the number
or percentage of cities it represents.
Similarly, the number or percentage of population living in different size classes
of towns or cities may also be portrayed in the form of urban pyramid. Generally,
urban geographers around the world, rigorously and successfully use these types of
3.4 Types of Diagrams in Data Representation 165
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166 3 Diagrammatic Representation of Geographical Data
Fig. 3.7 Ecological pyramid (Pyramid of numbers)
Fig. 3.8 Urban pyramid showing the percentage of towns in different size classes in India
urban pyramids to understand and explain the structural characteristics of the urban
system of any country or region.
3.4.1.3 Difference Between Histogram and Bar Diagram
Though histogram and bar diagram are nearly similar in appearance, there are some
specific and important differences between them.
3.4 Types of Diagrams in Data Representation 167
Table 3.8 Database for urban pyramid (Size class distribution of towns in India, 2011)
Size class Number of
towns
Percentage (%)
of towns
Scale selected Length of
the bar (cm)
1951 2011 1951 2011 1951 2011
Class-I (>100,000) 69 505 3.11 6.36 1 cm to 5% towns 0.62 1.27
Class-II (50,000–100,000) 107 605 4.82 7.63 0.96 1.53
Class-III (20,000–49,999) 363 1,905 16.36 24.01 3.27 4.80
Class-IV (10,000–19,999) 571 2,233 25.73 28.15 5.15 5.63
Class-V (5000–9999) 737 2,187 33.21 27.57 6.64 5.51
Class-VI (<5000) 372 498 16.76 6.28 3.35 1.26
Total 2,219 7,933 100 100
Source Census of India
Histogram Bar diagram
1. Histogram refers to the graphical
representation of statistical data by rectangles or
bars drawn on a horizontal baseline to show the
frequency of numerical data
1. Bar diagram is the diagrammatic
representation of statistical data in the form of
bars to compare different categories of data
2. It indicates the distribution of different
continuous variables
2. It indicates the comparison of different
discontinuous or discrete variables
3. It represents quantitative data 3. It represents categorical data
4. Class boundary is shown along the x-axis and
the number of observations (frequency) is
shown along the y-axis
4. Time, place or other categories are shown
along the x-axis while the amount or quantity
of information is shown in the y-axis
5. Bars or rectangles are adjoining or
continuous, i.e. there is no space between bars
5. Bars are discontinuous, i.e. there is equal
space between bars
6. The height of each bar is directly proportional
to the frequency of the corresponding class
6. Lengths or heights of bars are directly
proportional to the amount or quantity of
information they represent
7. Data are grouped together so that they turn
into continuous or are considered as ranges
7. Data are taken as individual entities
8.The width of the bars is the same in equal
class size but different in unequal class size
frequency distribution
8. The width is same for all the bars
9. It is difficult and impossible to reorder the
bars
9. Bars can be easily reordered
10. More than one frequency distribution can’t
be represented at a time
10. More than one component or variable can
be easily represented at a time in a compound
or complex bar diagram
168 3 Diagrammatic Representation of Geographical Data
3.4.2 Two-Dimensional Diagrams
Unlike one-dimensional diagrams in which only the length is considered, in two-
dimensional diagrams the length, as well as the breadth are taken into consideration.
Thus, in two-dimensional diagrams the concept of area is very significant, called
area diagrams or surface diagrams. Important two-dimensional diagrams are given
in the following sub-sections.
3.4.2.1 Rectangular Diagram
Rectangular diagram, an important two-dimensional method, may be used when
two or more quantities are to be compared and each quantity is again sub-divided
into various constituent parts (Saksena 1981) (Table 3.9). These are analogous to
compoundbar diagrams as the length of bars are directly proportional to the quantities
they indicate but the area of the rectangles and their constituent parts are kept in
proportion to the values. Generally, the rectangles are placed side by side to make
them comparable. In the case of the representation of two or more sets of data, if the
scale is kept the same, the computation would be easier for construction.
In rectangular diagram, data may be represented in two ways: (i) representation
of the actual figures as they are given (Fig. 3.9) and (ii) by converting the actual
figures into percentages (Fig. 3.10). The percentage sub-divided rectangular diagram
Fig. 3.9 Rectangular
diagram showing the area of
irrigated land (hectares) by
different sources in India
3.4 Types of Diagrams in Data Representation 169
Fig. 3.10 Rectangular
diagram showing the area of
irrigated land (%) by
different sources in India
Table 3.9 Calculations for rectangular diagram (Area of irrigated land by different sources of
irrigation in India)
Sources of
irrigation
1950–1951 2000–2001
Irrigated area
(thousand
hectares)
% Cumulative % Irrigated area
(thousand
hectares)
% Cumulative %
Canals 8,295 44.0 44.0 15,790 28.98 28.98
Wells and tube
wells
5,980 31.7 75.7 33,275 61.07 90.05
Tanks 3,610 19.1 94.8 2,525 4.63 94.68
Others 970 5.2 100 2,900 5.32 100
Total 18,855 100 54,490 100
Source Statistical Abstracts of India, 2005–2006 and Husain, 2014
is more popular and acceptable than the absolute sub-divided rectangular diagram
as the former enables the data easily comparable on a percentage basis. Different
colours or dotting or crossings may be used to distinguish the constituent parts of
the rectangles.
Since the total irrigated land area in 1950–1951 and 2000–2001 are 18,855 and
54,490 thousand hectares, respectively, the width of the rectangles will be in the ratio
of 18,855:54,490, i.e. 1:2.90.
3.4.2.2 Triangular Diagram
Triangular diagram is an important two-dimensional diagram which represents a
series of equilateral triangles in which the size and area of each triangle (‘a’) is
directly proportional to the quantity (‘q’) it indicates (Sarkar 2015). Theoretically,
170 3 Diagrammatic Representation of Geographical Data
a α q (3.1)
or a = k.q (k = proportionality constant)
If the side of the equilateral triangle having area ‘a’ is ‘l’, then
√
3
4
l2 = a (3.2)
[Area of an equilateral triangle with side length ‘l’ =
√
3
4 l2]
√
3
4
l2 = k.q(a = k.q)
l2 = 4k.q√
3
l =
√
k
4q√
3
(3.3)
So, for any item (i), corresponding to the quantity (q), the side of the equilateral
triangle (l) can be represented by the following equation:
li =
√
4qi√
3
(3.4)
For the drawing of triangles, a suitable scale should be selected carefully (Table
3.10) so that an individual triangle does not become too small or too large with
respect to the given base map. Each triangle should be drawn within the boundary
of the respective administrative unit of the base map, but in case of unavailability of
the map, the triangles should be drawn on the same baseline maintaining uniform
distance between them. The diagrammatic representation of proportional scale must
contain at least three equilateral triangles showing approximately the largest,medium
and smallest quantities of the given data (Fig. 3.11).
3.4.2.3 Square Diagram
Square diagram, another important two-dimensional diagram, represents a series of
squares in which the size of each square is directly proportional to the quantity it
signifies. Unlike rectangular diagram, in which the representation of widely varied
data is difficult, in square diagram any quantity of data can be easily and simply
represented.
3.4 Types of Diagrams in Data Representation 171
Table 3.10 Worksheet for triangular diagram (Geographical area of selected biosphere reserves in
India)
Biosphere reserve Geographical
area (sq. km)
li =
√
4qi√
3
Scale selected Length of the
side of the
triangle (cm)
Sundarban 9,630 149.13 1 cm to 80 units 1.86
Manas 2,837 80.94 1.01
Nilgiri 5,520 112.91 1.41
Gulf of Mannar 10,500 155.72 1.95
Simlipal 4,374 100.50 1.26
Panchamarhi 4,928 106.68 1.33
For proportional
scale
Largest 11,000 159.38 1.99
Medium 6,750 124.85 1.56
Smallest 2,500 75.98 0.95
Source Geography of India by Majid Husain, 2014
Fig. 3.11 Triangular diagram (Geographical area of selected biosphere reserves in India)
The drawing of the square diagram is based on the theory that area of each square
(‘a’) is directly proportional to the quantity it represents (‘q’). Therefore.
a α q (3.5)
or, a = k.q (k = proportionality constant)
If the length of the side of a square having area ‘a’ be ‘l’, then
l2 = a (3.6)
172 3 Diagrammatic Representation of Geographical Data
Table 3.11 Worksheet for square diagram (Population of selected million cities of India, 2011)
Name of the Urban
Agglomeration
Population li = √
Pi Scale selected Length of the side
of the square (cm)
Delhi 16,314,838 4039.16 1 cm to 1500 units 2.69
Greater Mumbai 18,414,288 4291.19 2.86
Kolkata 14,112,536 3756.66 2.50
Chennai 8,696,010 2948.90 1.96
Bangalore 8,499,399 2915.37 1.94
Hyderabad 7,749,334 2783.76 1.85
Ahmedabad 6,240,201 2498.04 1.66
For proportional
scale
Largest 20,000,000 4472.13 2.98
Medium 12,500,000 3535.53 2.36
Smallest 5,000,000 2236.07 1.49
Source Government of India, Ministry of Information: Production Division, India (2012), New
Delhi, pp. 77–78 and Geography of India by Majid Husain, 2014
[Area of a square with side length ‘l = l2]
or l2 = k.q(a = k.q)
l = √
k.q (3.7)
So, for any item (‘i’), corresponding to the quantity (‘q’), the length of the side
of the square (‘l’) can be explained by the following equation:
li = √
k.qi (3.8)
For the simplification of the calculation and easy understanding,
√
k.qi may be
written as
√
Pi in the calculation Table 3.11.
For the drawing of the squares, a suitable scale should be selected carefully so that
the individual square does not become too small or too large with respect to the given
base map. Each square should be drawnwithin the boundary of the respective admin-
istrative unit of the base map. In case of unavailability of the map, the square should
be drawn on the same baseline maintaining a uniform distance between them. The
diagram must contain a proportional scale having at least three squares representing
roughly the largest, medium and smallest quantities of the given data (Fig. 3.12).
3.4.2.4 Circular Diagram
Like triangular and square diagram, circular diagram is also an important two-
dimensional diagram. It consists of a series of circles in which the size or area of
each circle is directly proportional to the quantity it represents. In this diagram, both
3.4 Types of Diagrams in Data Representation 173
Fig. 3.12 Square diagram (Population of selected million cities of India, 2011)the total figure and the component parts or sectors can be easily represented. The
area of each circle is directly proportional to the square of its radius. The working
principle for the construction of circular diagram is that the area of a circle (‘a’) is
directly proportional to the quantity (‘q’) to be represented. Empirically,
a α q (3.9)
or a = k.q (k = proportionality constant)
If the radius and area of a circle are ‘r’ and ‘a’, respectively, then
�r2 = a (3.10)
[Area of a circle with radius ‘r ’ = �r2].
or �r2 = k.q (a = k.q)
r2 = k.
q
�
r =
√
k
q
�
(3.11)
So, for any item (‘i’), corresponding to the quantity (‘q’), the radius of the circle
(‘r’) can be explained by the following equation:
ri =
√
k
qi
�
(3.12)
174 3 Diagrammatic Representation of Geographical Data
Table 3.12 Worksheet for simple circular diagram (Cropping pattern in India, 2010–2011)
Crops Area in million
hectares
ri =
√
Ti
�
Scale selected Radius of the
circle (cm)
Rice 45.0 3784.70 1 cm radius to
1500 units
2.52
Wheat 29.25 3051.32 2.03
Jowar 10.4 1819.46 1.21
Bajra 8.8 1673.66 1.12
Maize 6.4 1427.30 0.96
Gram 6.3 1416.10 0.94
Pulses 21.1 2591.59 1.73
For proportional
scale
Largest 45 3784.70 2.52
Medium 25 2820.95 1.88
Smallest 5 1261.57 0.84
Source Government of India, Ministry of Information: Production Division, India (2012), New
Delhi, pp. 77–78 and Geography of India by Majid Husain, 2014
For the simplification of the calculation and easy understanding,
√
k qi
�
may be
written as
√
Ti
�
in the calculation table.
Therefore, for the construction of circular diagram, radii of the circles are obtained
by dividing the absolute figures (respective aggregate values) by the value of pie (�)
and taking square root (Tables 3.12 and 3.13). A suitable scale should be selected
for the drawing of circular diagram so that an individual circle does not become too
large or too small in size. A proportional scale must be shown diagrammatically with
at least three circles roughly representing the largest, medium and smallest values of
the given data (Figs. 3.13 and 3.14).
Based on the nature of data, circular diagrams are of two types:
(i) Simple circular diagram or proportional circles and (ii) sub-divided circle or
compound circular diagram or angular diagram or pie diagram or wheel diagram.
Simple Circular Diagram
When the data consists of only one component (Table 3.12) then simple circles are
constructed in which each circle represents a single value. The same principles are
followed for the construction of simple circular diagram as that of constructing
square diagram. The radii of the circles are taken in proportion to the square roots of
the given figures following the formula mentioned earlier (Eq. 3.12). In the case of
large values of the radii, they are converted to convenient small values by dividing
the square roots by a suitable common value (Table 3.12). After the computation of
the radii, the circles are drawn carefully keeping in mind that the centres of different
3.4 Types of Diagrams in Data Representation 175
Fig. 3.13 Simple circular diagram (Cropping pattern in India, 2010–2011)
Fig. 3.14 Pie diagram (Consumption of different fertilizers in India)
176 3 Diagrammatic Representation of Geographical Data
circles put side by side with each other or below each other must be located on the
same straight line (Fig. 3.13).
Angular Diagram or Compound Circular Diagram or Pie Diagram or Wheel
Diagram
When the data is composed of a total value and two or more component parts (Table
3.13) then compound circular diagram or pie diagram is constructed (Fig. 3.14).
The area of the circle represents the total value and the different sub-divisions or
angular sectors of the circle represent the different component parts. In this diagram,
360° angles, made at the centre of the circle, correspond to the total value which is
again sub-divided into a number of smaller angles or angular sectors (Fig. 3.14). The
degrees of these angular sectors would be directly proportional to the values of the
component parts (Table 3.13).
The angular or sectoral divisions of different component parts within the circle
may be computed by the following formula:
sc1 = 360◦
q
× c1 (3.13)
where sc1 = degrees of an angular segment for component 1, q = total quantity of
all the component parts, c1 = quantity of component 1
Here, c1 + c2 + c3 + · · · + cn = q (3.14)
and sc1 + sc2 + sc3 · · · + scn = 360◦ (3.15)
For the drawing of the angular segments in pie diagram, it is essential to follow a
number of logical principles, arrangements and patterns or sequences. As a common
procedure, different angular sectors are started to be drawn from a fixed line (gener-
ally, from the radius drawn duewest or north) and are arranged according to their size,
with the largest at the top and the others running sequentially clockwise (Fig. 3.14).
In the pie diagram, the circles and the angular segments are drawn with the help
of a compass and a protector. Different angular sectors of the circles representing
different components should be neatly coloured or be clearly marked by different
signs and symbols in order to make the diagram attractive. A well-organized legend
of colours or signs and symbols should be provided to make the diagram meaningful
and understandable.
3.4 Types of Diagrams in Data Representation 177
Fig. 3.15 Percentage pie diagram showing the consumption of different fertilizers in India
Pie Diagram in Percentage
In the case of comparison of data, percentage representation of pie diagram is
more appropriate and useful than absolute representation. Because in a series of
pie diagrams, it is needed to represent the larger total figure by a larger circle and the
smaller total figure by a smaller circle. This type of representation involves difficul-
ties and complications of two-dimensional comparisons. But, if the pie diagrams are
constructed based on percentage value, then all the absolute totals (including larger
and smaller) are considered to be 100 percentages, and hence the size of all the pie
diagrams become equal (Fig. 3.15).
For the construction of percentage pie diagram, all the component values are
converted into percentage with respect to the total value (Table 3.13). In such a
situation, 100% value is represented by 360° angular value at the centre of the circle,
and hence 1% value is represented by 3.6◦ ( 360
◦
100 ) angular value. For example, if ‘P’ is
the percentage value of a certain component, then it will be represented by (3.6◦ ×P)
degrees as the corresponding angular value.
178 3 Diagrammatic Representation of Geographical Data
Ta
bl
e
3.
13
W
or
ks
he
et
fo
r
pi
e-
di
ag
ra
m
(C
on
su
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of
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rt
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in
In
di
a,
la
kh
to
nn
es
)
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ea
r
C
on
su
m
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n
of
fe
rt
ili
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rs
(l
ak
h
to
nn
es
)
To
ta
l
R
ad
iu
s
of
th
e
ci
rc
le
r i
=
√ T
i
�
Sc
al
e
se
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ct
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R
ad
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s
of
th
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ci
rc
le
(c
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68
Y
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(D
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To
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l(
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on
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of
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(%
)
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%
)
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3.4 Types of Diagrams in Data Representation 179
Disadvantages of Pie Diagrams
Though pie diagram is frequently used as a common statistical technique, the
construction of this diagram is time-consuming compared to other diagrams espe-
cially than bar diagram. Accurate reading and interpretation of a pie diagram become
very difficult, particularly when the circles are divided into a large number of compo-
nent sectors or the variation between these components is very little. Generally, it is
not suitable to construct a pie diagram when the data is composed of more than five
or six components or categories. In the case of eight or more components, it becomes
very difficult and confusing to differentiate the relative quantities of them represented
in the pie diagram, especially when several small sectors having approximately the
same size are there. Generally, pie diagram appears upon comparison inferior to other
diagrams and curves like compound bar diagram or a group of curves.
3.4.2.5 Doughnut Diagram
Like pie diagram, doughnut diagram displays the relationship of component parts
to a whole, but it is capable of containing more than one data series (Table 3.14). In
this diagram, each set of data is represented by a ring in which the first data set is
displayed at the centre and the last data set towards the outside. Similar to the pie
diagram, in doughnut diagram component items are represented by individual slices
(Fig. 3.16). If we want to demonstrate the changes of different component parts of
something, then doughnut diagram will be more appropriate than the other type of
diagrams like bar or pie diagrams. Thus, it gives a birds-eye view of the relative
changes in each component part of the data series.
A doughnut diagram demonstrates different category groups, series groups and
series values in the form of doughnut slices. The size of each slice is directly propor-
tional to the value it represents in proportion to the total values. In the doughnut’s
hole at the centre, the data labels and the totals can be displayed to make it easier
to compare different segments. If the data labels are represented in percentage then
each ring will total 100%.
Doughnut diagrams are of two types: simple doughnut and exploded doughnut.
An exploded doughnut diagram is identical to a simple doughnut diagram but the
only difference is that in the exploded doughnut, the slices are moved away from the
centre of the diagram, resulting in a gap between the doughnut slices.
When the Doughnut Diagram Should Be Used
1. If we want to represent more than one data series.
2. No negative value in the data series exists.
3. When the data don’t have more than seven or eight component parts.
180 3 Diagrammatic Representation of Geographical Data
Fig. 3.16 Doughnut diagram (Area under different land uses in selected districts of West Bengal)
Table 3.14 Database for doughnut diagram (Area under different land uses in selected districts of
West Bengal)
Name of the
districts
Area (in thousand acres)
Agricultural
land
Forest land Waste land Water bodies and
barren land
Land under
miscellaneous
use
Purulia 336.06 75.05 49.27 68.32 87.05
Bankura 367.02 66.02 22.17 75.16 100.2
Paschim
Medinipur
467 51.06 57 82 175
Birbhum 304 47 32 52 116
Jalpaiguri 396 82.16 30 69.20 141
3.4 Types of Diagrams in Data Representation 181
Advantages and Disadvantages of Doughnut Diagram
The major advantages and disadvantages of using doughnut diagram include:
Advantages
1. Multiple data sets can be easily represented in a doughnut diagram.
2. Using this diagram, we can get a birds-eye view of the relative changes of
different component items within the data series.
3. Comparison of different component parts using different slices becomes easy.
4. The blank space inside a doughnut diagram can be used to show the information
which the diagram actually indicates.
Disadvantages
1. Due to their circular shape, doughnut diagrams are not easy to understand,
especially when they represent numerous sets of data.
2. In doughnut diagram, the volume of data is not represented accurately by the
proportions of outer rings and inner rings. The data points on inner rings may
come into view smaller than data points on outer rings though the actual values
may be larger or the same. Because of this, it is necessary to display the values
or percentages of them in data labels to make them more accurate and useful.
Difference Between Pie Diagram and Doughnut Diagram
Though pie diagram and doughnut diagram both display the relationship of
component parts to a whole but these two are different under the following heads:
Pie diagram Doughnut diagram
1. Demonstrates the size differences of
component parts to a whole of one data series
only. Thus, it is difficult to represent multiple
data sets in pie diagram
1. Size differences of component parts to a
whole of multiple data sets can be easily
represented in a doughnut diagram
2. Proportions of areas of the slices to one
another and to the diagram as a whole are
significant to compare multiple pie diagrams
together
2. Focus more on understanding the length of
the arcs of rings rather than comparing the
proportions of areas between slices
3. The inner cut out percentage defaults to 0 for
pie diagrams
3. The inner cut out percentage defaults to 50
for doughnuts
4. Less space-efficient, as no blank space exists
inside a pie diagram
4. Space-efficient, as the blank space inside a
doughnut diagram can be used to show
information inside it
5. Unable to give a birds-eye view of the
relative changes of different component parts
within the data set
5. It can give a birds-eye view of the relative
changes of different component parts within
multiple sets of data
6. Comparison of different component parts is
difficult
6. Comparison of different component parts
using different slices becomes easy
182 3 Diagrammatic Representation of Geographical Data
3.4.3 Three-Dimensional Diagrams
Three-dimensional diagrams are those in which three things, namely length,
width (breadth) and height are taken into consideration. Those diagrams are also
known as volume diagrams. Some important three-dimensional diagrams are in the
following sub-sections.
3.4.3.1 Cube Diagram
Cube diagram is an important three-dimensional diagram which is suitably
constructed for the representation of the items having wide differences between
them, say, smallest and the largest values are in the ratio of 1:1000 (Saksena 1981).
In this diagram, the volumes of all cubes would be in the same proportion as the ratio
of the actual data given. The construction of cube diagram is based on the theory that
the volume of cube (‘v’) is directly proportional to the quantity (‘q’) it represents.
Thus,
v α q (3.16)
or v = k.q (k = proportionality constant)
If the length of side and volume of a cube are ‘l’ and ‘v’, respectively, then
l3 = v (3.17)
[Volume of a cubewith side length ‘l’ = l3]
or l3 = k.q(v = k.q)
l = 3
√
k.q (3.18)
So, for any item (‘i’), corresponding to the quantity (‘q’), the length of the side
of the cube (‘l’) can be explained by the following equation:
li = 3
√
k.qi (3.19)
For the simplification of the calculation and easy understanding, 3
√
k.qi may be
written as 3
√
Pi in the calculation table.
For constructing cube diagram, at first the cube roots of the data should be calcu-
lated with the help of logarithms. Then the logarithmic figures will be divided by the
value 3 and the antilog of thisvalue will indicate the cube root. By this technique,
the sides of the cubes should be made in proportion to the cube roots of the given
figures. If the sides of the cubes are large enough, then they should be reduced to a
convenient size by dividing the values of cube roots by a common value.
3.4 Types of Diagrams in Data Representation 183
Fig. 3.17 Steps of construction of cube diagram
Steps to Construct Cube Diagram
Following steps should be followed to construct cube diagram:
1. At first, a square should be drawn with the length of the side of the cube to be
portrayed (Fig. 3.17I).
2. Another square of the same size should be drawn with its lower-left corner
coinciding with the centre of the first square. Thus the corresponding sides of
the two squares become parallel to each other (Fig. 3.17II).
3. Then the left and right upper corners and lower right corners of both the squares
should be joined by straight lines (Fig. 3.17III).
4. Lastly, the left-hand side and the lower side of the second squares should be
erased and the resultant figure should be a cube (Fig. 3.17IV).
Scale for the drawing of cube diagram should be selected in such a way that none
of the individual cubes is too large or too small in size. In case of unavailability of
map, the cubes should be drawn on the same baseline with equal intervening space. A
proportional scale must be shown diagrammatically with at least three cubes roughly
representing the largest, medium and smallest values of the given data (Fig. 3.18).
Table 3.15 shows the population of themain seven tribal groups in India according
to the 2011 census and data is represented using cube diagram in Fig. 3.18.
184 3 Diagrammatic Representation of Geographical Data
Fig. 3.18 Cube diagram (Population of main seven tribes in India)
Table 3.15 Worksheet for cube diagram (Population of main seven tribes in India, 2011)
Name of tribes Population li = 3
√
Pi Scale selected Side of the cube
(cm)
Bhil 12,689,952 233.25 1 cm to 100 units 2.33
Gond 10,859,422 221.45 2.21
Santal 5,838,016 180.06 1.80
Mina 3,800,002 156.05 1.56
Naikda 3,344,954 149.55 1.50
Oraon 3,142,145 146.47 1.46
Sugalis 2,077,947 127.61 1.28
For proportional
scale
Largest 13,000,000 235.13 2.35
Medium 7,500,000 195.74 1.96
Smallest 2,000,000 125.99 1.26
Source Census of India
N.B. Cube roots may be calculated as follows:
Cube root of a number = Antilog
(
Log of the number
3
)
3.4 Types of Diagrams in Data Representation 185
3.4.3.2 Sphere Diagram
Sphere diagram is another important three-dimensional diagram consisting of a
series of spheres which are constructed based on the principle that the volume of
each sphere (‘v’) is directly proportional to the quantity (‘q’) it represents. Thus,
v α q (3.20)
or v = k.q (k = proportionality constant)
If the radius and volume of the sphere are ‘r ’ and ‘v’, respectively, then
4
3
�r3 = v (3.21)
[Volume of a sphere with radius‘r ’ = 4
3�r3]
or 4
3�r3 = k.q(v = k.q)
r3 = k
3q
4�
r = 3
√
k
3q
4�
(3.22)
For any item (‘i’), corresponding to the quantity (‘q’), the radius of the sphere
(‘r ’) can be expressed by the following equation:
ri = 3
√
k
3qi
4�
(3.23)
For the simplification of the calculation and easy understanding, 3
√
k 3qi
4� may be
written as 3
√
3qi
4� in the calculation Table 3.16.
For the drawing of sphere diagram, the scale should be selected carefully so that
none of the individual spheres becomes too large or too small in size. Spheres are
generally drawn within the boundary of the administrative unit of the given map.
In the case of the unavailability of maps, the spheres can be drawn on the same
baseline with equal distance between them. The diagrammust contain a proportional
scale having at least three spheres representing roughly the largest, medium and
smallest quantities of the given data. Curved lines should be drawn carefully on the
surface of the sphere to represent the parallels and meridians so that they appear as
three-dimensional diagrams involving volumes (Fig. 3.19).
186 3 Diagrammatic Representation of Geographical Data
Fig. 3.19 Sphere diagram (Urban population of selected states in India, 2011)
Table 3.16 Worksheet for sphere diagram (Urban population in selected states in India, 2011)
Name of the state Urban
population
ri = 3
√
3qi
4� Scale selected Radius of
the sphere (cm)
Uttar Pradesh 4,44,70,455 219.78 1 cm to 120 units 1.83
Maharashtra 5,08,27,531 229.79 1.91
Bihar 1,17,29,609 140.95 1.17
West Bengal 2,91,34,060 190.88 1.59
Andhra Pradesh 2,83,53,745 189.16 1.58
Madhya Pradesh 2,00,59,666 168.56 1.40
Tamil Nadu 3,49,49,729 202.82 1.69
For proportional
scale
Largest 6,00,00,000 242.86 2.02
Medium 3,50,00,000 202.92 1.69
Smallest 1,00,00,000 133.65 1.11
Source Census of India
3.4.4 Other Diagrams
3.4.4.1 Pictograms
Pictograms are another very important and popular technique in which statistical
or geographical data are represented by various pictorial symbols such as sacks,
bales, tanks, discs etc. (Singh and Singh 1991) (Table 3.17). This is not the abstract
3.4 Types of Diagrams in Data Representation 187
Table 3.17 Data for pictograms (Production of wheat in different years in India)
Year Wheat (Ravi) production
(million tonnes)
Scale selected Number of pictorial
symbols
2004–05 68.6 One pictorial symbol
represents 10 million
tonnes of wheat
7
2010–11 86.9 9
2011–12 94.9 10
2012–13 93.5 10
2013–14 95.9 10
Year Number of Sacks
2004–05
2010–11
2011–12
2012–13
2013–14
representation of data like lines or bars but it actually depicts the kind of data wewant
to represent. This method is more suitable and useful to the layman in representing
different statistical and geographical data. In a pictogram, a number of pictures and
symbols are drawn to represent different types of data.
Principles of Drawing of Pictograms
The following points should be kept in mind while a pictogram is constructed:
a. Pictorial symbols should usually be of the same size and equal in value. Each
picture represents a fixed number of units or a particular quantity (Table 3.17).
b. All the pictorial symbols should be self-explanatory. For example, if we want
to represent the male population then the symbol should undoubtedly indicate
the male population.
c. A symbol must indicate the general idea only (like a boy, girl, truck, bus etc.)
but not the individual of a species (not Hitler or Akbar etc.).
d. All the pictorial symbols drawn should be simple, clear, concise, interesting,
easy to understand and easily distinguishable from every other symbol.
e. Variations in quantities or numbers should be represented by fewer or more
symbols, but not by smaller or larger symbols (Table 3.17).
f. All the symbols should be drawn suitably with the size of the paper, i.e. they
should not be too small or too large in size.
188 3 Diagrammatic Representation of Geographical Data
g. Generally, the pictorial symbols are drawn horizontally (side by side), but they
may also be drawn vertically.
h. The quantity or the number of units represented by each pictorial symbol should
be clearly mentioned.
i. Part of a picture may be used to represent the fraction of the total value
represented by each picture.
Examples To represent 60 million tonnes of wheat produced in a region, six sacks
may be heaped together when one sack is supposed to represent 10 million tonnes of
wheat. Similarly, to represent 80 aeroplanes in an airport, eight symbols of aeroplane
may be drawn together when one aeroplane symbol is supposed to represent 10
aeroplanes.
Advantages and Disadvantages of the Use of Pictograms
The major advantages and disadvantages of the use of pictograms are:
Advantages
(1) Pictograms are more attractive and impressive than other types of diagrams.
When it is needed to attract the attention of the masses (people) such as in
exhibitions, fairs etc. then pictograms are very popular in use.
(2) Facts and events represented in a pictorial form are usually rememberedlonger
than representation in tables or other diagrammatic forms.
(3) Comparison of different data sets becomes easy when they are represented in
pictorial form.
Disadvantages
(1) Drawing of pictograms is very difficult as it requires some artistic sense.
(2) Pictograms provide only the overall idea of any fact or event, but they do not
offer their minute details.
(3) In a pictogram it is required to use one symbol to correspond to a fixed quantity
or fixed number of units which may also create problems. For example, if one
symbol represents a five lakh population, then the question is that how many
symbols are required to represent a population of 27.3 lakhs.
3.4.4.2 Kite Diagrams
It represents the change of the percentage cover of geographical phenomena or
characteristics over distance. It is most frequently used to show the changes in the
percentage cover of different plant species along the environmental gradient (change
of environmental conditions with distance).
For example, the change of plant species from the edge of a footpath or along a
sand dune transect (Fig. 3.20 and Table 3.18), along a coastline etc. can be easily
represented in kite diagram.
3.4 Types of Diagrams in Data Representation 189
Ta
bl
e
3.
18
D
at
ab
as
e
fo
r
ki
te
di
ag
ra
m
(N
um
be
r
of
ve
ge
ta
tio
n
sp
ec
ie
s
al
on
g
th
e
sa
nd
du
ne
tr
an
se
ct
s)
N
am
e
an
d
nu
m
be
r
of
sp
ec
ie
s
D
is
ta
nc
e
in
m
et
re
(F
ro
m
se
a
to
in
la
nd
)
0
10
20
30
40
50
60
70
80
90
10
0
C
ou
gh
gr
as
s
63
(4
0%
)
46
(2
9%
)
24
(1
5%
)
15
(1
0%
)
8
(5
%
)
0
0
0
0
0
0
D
an
de
lio
n
12
(6
%
)
11
(5
%
)
20
(9
%
)
34
(1
6%
)
55
(2
6%
)
32
(1
5%
)
21
(1
0%
)
10
(5
%
)
10
(5
%
)
5
(2
%
)
2
(1
%
)
M
ea
do
w
gr
as
s
0
(0
%
)
0
(0
%
)
0
(0
%
)
0
(0
%
)
0
(0
%
)
12
(6
%
)
14
(8
%
)
24
(1
3%
)
32
(1
7%
)
45
(2
4%
)
60
(3
2%
)
190 3 Diagrammatic Representation of Geographical Data
Fig. 3.20 Kite diagram showing the number of vegetation species along the sand dune transect
Procedures to Draw Kite Diagrams
Kite diagrams are drawn using the following steps:
1. At first, we need to draw a scale line to represent the distance covered in the
survey.
2. One row is needed to represent each type of plant species.
3. Each and every row requires to follow the same scale and will be wide enough
(sufficiently apart from the others) to allow 100% for each plant species and
type.
4. Then we have to draw a line through the middle (central line) of each row
representing the value ‘0’.
5. At each point of the survey, the percentage value is plotted on both sides above
and below the central line to achieve symmetry.
6. Then the obtained points are connected for each row and it gives the diagram
having a kite-like appearance.
7. The area between the kite lines are then shaded (Fig. 3.20).
Advantages and Disadvantages of Using Kite Diagrams
Use of kite diagram to represent geographical data has some advantages as well as
some disadvantages:
Advantages
1. Very easy to understand and interpret.
3.4 Types of Diagrams in Data Representation 191
2. Clearly shows the changes of different geographical phenomena over distance.
3. Shows the density and distribution of geographical variables.
Disadvantages
1. Not suitable for the representation of all types of data.
2. Time-consuming to plot manually.
References
Saksena RS (1981) A handbook of statistics. Indological Publishers & Booksellers
Sarkar A (2015) Practical geography: a systematic approach. Orient Blackswan Private Limited,
Hyderabad, Telengana, India. ISBN: 978-81-250-5903-5
Sharma PD (1975) Ecology and environment. Rastogi Publications, Gangitri, Shivaji Road,Meerut-
250002, ISBN: 978–93–5078–122–7
Singh RL, Singh RPB (1991) Elements of practical geography. Kalyani Publishers, New Delhi
Chapter 4
Mapping Techniques of Geographical
Data
Abstract Map is the simplified depiction of the geographical data about the whole
earth or a part of it on a piece of plane surface or paper for better understanding
of their cartographic characteristics. Maps are the basic tools for geographers and
researchers for the visualization of geographic data and understanding their spatial
relationships. This chapter explains the basic cartographic terminologies such as
Geodesy, Geoid, Spheroid, Datum, Geographic co-ordinate system, Surveying and
levelling, Traversing, Bearing, Magnetic declination, Magnetic inclination etc. in a
lucid manner with suitable illustrations. It includes the detailed classification and
discussion of all types of maps based on their scale and purposes (contents) of
preparing the map with special emphasis on Indian Topographical Sheets. All picto-
rial andmathematicalmethodsof representationof relief havebeen explained indetail
with suitable examples and illustrations. Various types of distributional thematic
maps have been analyzed with suitable examples emphasizing their suitable data
structure, necessary numerical calculations,methods and principles of their construc-
tion, proper illustrations and advantages and disadvantages of their use. Step-by-step
and systematic discussion of the methods of construction of maps makes them easy
and quickly understandable to the readers and users. Emphasis has also been given
on the detailed discussion of techniques of measurement of direction, distance and
area on maps.
Keywords Mapping technique · Cartographic terminologies · Representation of
relief · Distributional thematic maps · Importance and uses of maps
4.1 Concept and Definition of Map
Maps are the basic tools for the visualization of geographic data and understanding
their spatial relationships. A map is a simplified representation of the whole or part
of the earth on a piece of plane surface or paper. It is a two-dimensional depiction of
the three-dimensional earth. As the representation of all aspects of the earth’s surface
in their actual size and form is quite impossible, a map is drawn at a reduced scale.
Maps are drawn in such a way that each and every point on them truly corresponds
to the actual ground surface.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. K. Maity, Essential Graphical Techniques in Geography, Advances in Geographical
and Environmental Sciences, https://doi.org/10.1007/978-981-16-6585-1_4
193
http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-16-6585-1_4&domain=pdf
https://doi.org/10.1007/978-981-16-6585-1_4
194 4 Mapping Techniques of Geographical Data
Map can be defined as a reduced (scaled), generalized and explained depiction
(image) of objects, elements and events on the Earth or in space, constructed in a two-
dimensional plane surface or paper applying mathematically defined relationships
(i.e.maintaining correct relative locations, sizes and orientations). The term reduction
is related to the length scale of amap, which is the ratio between the accurate length in
amap and the corresponding length on ground. Generalization is an obvious outcome
of the reduction, as all the particulars cannot be represented in a map in the same
detail. The explanation tells us about themodes of expression and appearance through
the use of legend. Map, in other words, is the representation of the earth’s pattern as
a whole or a part of it, or the heavens on a two-dimensional flat surface following
suitable scale and projection using conventional symbols so that each and every point
on it truly corresponds to the actual terrestrial or celestial position (Fig. 4.2). Three-
dimensional maps can be made using the modern computer graphics only. Globes
are maps portrayed on the surface of a sphere.
Map illustrates information about the earth in a simple andvisualway. It serves two
functions; act a spatial database and a communication device. Basic map features say
to the user where an object or event is (its location) and what the object or event is (its
characteristics). The amount of information to be depicted on themap depends on: (a)scale of the map, (b) projection used, (c) methods of map-making (d), conventional
symbols and (e) skill and efficiency of the draughtsman or map maker etc.
4.2 Concept of Plan
A plan is the graphical representation of various aspects on or near the surface of
the earth on a horizontal plane to a large scale. The curvature of the earth is not
taken into consideration in plan. Therefore, it is suitable for smaller areas to avoid
distortions related to the curvature of the earth’s surface. The main purpose of a plan
is to precisely and unambiguously capture all types of geometric features of an area,
place, building or component (Fig. 4.1).
4.3 Difference Between Plan and Map
The differentiation between plan and map is not very easy as it is arbitrary in nature.
Main areas of distinction include:
Plan Map
1. Graphical representation of features on or
near the surface of the earth on a plane or flat
surface to a large scale. Scale is 1 cm = 10 m
or <10 m
1. Graphical representation of the whole or part
of the earth on a plane surface to a small scale
compared with the plan. Scale is 1 cm = 100 m
or >100 m
(continued)
4.3 Difference Between Plan and Map 195
(continued)
Plan Map
2. Plans are commonly used in technical fields
like architecture, engineering, planning etc.
2. Maps are commonly used to depict geography
3. Horizontal distances and directions are
generally shown on a plan
3. In a number of maps, vertical distances
(elevations) are also shown along with the
horizontal distances and directions. For
example, on a topographical map, elevations are
shown by contour lines
4. A plan is drawn for small areas. For
example, plan of a house, plan of a market
complex, plan of a college campus etc.
4. A map is drawn for large area. For example,
map of Asia, map of India, map of West Bengal
etc.
5. In plan, details are given in the form of
symbols
5. A map contains lots of important information
of the area
Fig. 4.1 Plan of a college campus
196 4 Mapping Techniques of Geographical Data
4.4 Elements of a Map
Several important elements are there that should be incorporated whenever a map is
prepared for the better understanding and interpretation of the map by the viewers.
A few maps may have more than this just basic information, but all maps should
contain five basic elements like Title, Grid, Scale, Legend and North Arrow. These
elements of a map have an important role to describe map details.
1. Title
Title is one of the fundamental features of a map and is very important because it lets
the viewers know the general subject matter of the map and what geographic area the
map represents. A short and catchy ‘title’ might be appropriate if the readers have
knowledge about the theme presented on the map. The suitable title, whether small
or long, should provide an answer to the viewers to their ‘What? Where? When?’
The title ‘Sediment yield in global rivers’ quickly says to the readers the theme and
location of the data represented in the map (Fig. 4.2).
Fig. 4.2 Elements of a map (Source Sediment yield in global rivers, Milliman and Meade 1983)
4.4 Elements of a Map 197
2. Grid
Geographic grid system or latitude and longitude marks are really very helpful to the
viewers to identify the exact location of a place or object onmap.A grid is represented
by a series of vertical and horizontal lines running across the map representing
longitudes and latitudes, respectively (Fig. 4.2). Latitude lines (parallels) run east–
west around the globe while the longitude lines (meridians) run north–south. The
points of intersection of parallels andmeridians are called co-ordinates. The parallels
and meridians are set up with letters and numbers indicating the values of latitudes
and longitudes.
On large-scale maps (objects and phenomena are shown in greater detail), the
grids are generally assigned with letters and numbers. Segments (boxes) of the grid
may be identified as A, B, C etc. across the top and 1, 2, 3 etc. across the left side
of the map. If a stadium is located in B4 box of the grid, and it is mentioned in the
index of the map, then the viewer easily finds the stadium by having a look at the
box where column B and row 4 cross.
3. Scale
The scale represents the relation between a specific distance on the map and the
actual distance in the real world, i.e. on the ground. Three main methods are there
to represent map scale such as (1) Statement or Verbal Scale (i.e. 1 cm on map is
equivalent to 5 km on ground or 1 inch on map is equivalent to 10 mile on ground
etc.), (2) Numeric or Ratio Scale (i.e. 1:10,000, it means that each one map unit
represents 10,000 units on the real world or a distance of one inch on the map equals
10,000 inches on real world or a distance of one cm on the map equals 10,000 cm on
real world) and (3) Graphical Scale (ratio of map distance and ground distance can
be shown graphically in the form of a scale bar like linear scale, diagonal scale etc.)
(Fig. 4.2). In case of computer-generated maps, the graphical form of representation
of scale is generally preferred. The maps that are drawn without following scale are
required to have a ‘Not to scale’ notation.
4. Legend
Cartographers use different symbols and colours to represent various geographic
features. For example, black dots to represent cities; various sorts of lines to represent
national and international boundaries, roads, rivers etc.; green colour for forest; blue
colour forwater etc. The legend is the key element of amap describing all unknown or
unique symbols and colours on the map. The legend acts as the decoder and explains
what the various symbols and colours used in the map represent. Descriptions spec-
ifying any colour combinations, symbology or categorization are clearly explained
in legend. Without the legend, it would be difficult for the viewers to understand the
symbols and colours used in the map.
For example, in a land-use/land-cover map, various land-use and land-cover cate-
gories are represented by different colours. The map would make no sense regarding
the land-use/land-cover pattern to the viewer until proper legend is given on the map.
In Fig. 4.2, the legend helps the viewer to understand the amount of annual sediment
yield in different river basin areas in the world.
198 4 Mapping Techniques of Geographical Data
5. North Arrow
The north arrow or compass rose indicates the orientation of the map, i.e. to indicate
the cardinal points (also called cardinal direction) of north, south, east and west (four
main points of a compass; detail discussion is given later) and maintain a connection
to the data frame (data frame is the part of the map displaying the data layers). As
that data frame is rotated, the north arrow also rotates with it. It helps the viewer to
recognize the right direction of the map as it is related to due north (cardinal direction
may also be indicated by first putting the word “due”). Though few exceptions are
there, but in most of the maps due north tends to be oriented towards the top of the
sheet (Fig. 4.2).
Other important elements of a map include:
6. Inset map or Locator
An Inset map or locator is a smaller map placed on the main map to further aid the
viewer. It is one type of reference map, which might show the relative location of
the main map. An inset map might also display a detailed, zoomed in portion of the
main map.
7. Labels
The words identifying the locations on the map are called labels. They show different
places (streets, rivers etc.) and establishments with their distinct names (Fig. 4.2).
8. Citation
The citation section of a map represents the metadata (description) of the map. This
is the area that contains information such as data sources, date of creation and map
projection etc. Citations facilitate the users to determine the use of the map for their
own purposes (Fig. 4.2).
4.5 History of Map-Making
Maps are not the discovery of the modern human being. The history of mapping
the earth is as older as the history